# Colloquia

Our colloquia feature researchers from around the world sharing their accomplishments and insights. The main organizers of these seminars are Yanqiu Guo  [Mathematics] and Sneh Gulati  [Statistics]. The talks are Thursdays from 3:45pm-4:45pm in DM 409A, if not specified. Some titles and abstracts are TBA.

## 2020 Colloquia

Speaker:  Sneh Gulati, FIU
Date: Mar 12

Speaker: Hadi Amini, FIU, School of Computing and Information Sciences
Date: Mar 5

[Spring Break]

Speaker:  Alex Iosevich, University of Rochester
Date:  Feb 20

Speaker: Aseel Farhat, Florida State University
Date: Feb 13

Speaker: Thomas Duyckaerts, Universite Paris-13
Date: Feb 11

Comparison of some test statistics for testing the regression coefficients in presence of multicollinearity: A simulation study

Speaker: Golam Kibria, FIU
Date: Feb 6

Abstract: This paper studied forty different ridge regression t-type tests of the individual coefficients of a linear regression model. Since a theoretical comparison among the test statistics is not possible, a simulation study has been conducted to evaluate their performances with respect to their empirical sizes and powers under different settings. It is evident from simulation results is that many of the proposed tests have type I error rates close to the 5% nominal level and have considerable gain in powers over the ordinary OLS t-type test. It also observed that tests based on ridge estimators KHKB, KKibMED, KKibGM , KM5, KKSMAX,  KK12  and KD4 performed better than the rest of the estimators in terms of achieving higher power gains while maintaining a 5 % nominal size. We therefore recommend them to statistical practitioners. Some possible future related research will be discussed.

Speaker:  Xi Huo, University of Miami
Date:  Jan 30

Speaker:  Benjamin Dodson, Johns Hopkins University
Date: Jan 23

#### Arrangements of Circles and Spheres leading to Convex Hulls with Minimal Boundaries

Speaker:  Prof. Josef Kallrath, Department of Astronomy, University of Florida
Date:  Friday, Jan 17, 2020
Time:  2pm-3pm
Room:  DM 409A

## Past Years

• 2019

#### Centroidal Voronoi Tessellations in 3D and Applications

Date: Dec 5 , 2019
Time:  3:45pm - 4:45pm
Room: DM 409A

Centroidal Voronoi Tessellations (CVT) are tessellations using Voronoi regions of their centroids. CVTs are useful in a variety of fields, such as data compression, optimal quadrature, optimal quantization, clustering, and optimal mesh generation. Many patterns seen in nature, such as the Giant’s Causeway, the cells of the cornea, and the honeycomb, are closely approximated by a CVT.

This is closely related to Gersho’s conjecture, which states that there exists an asymptotically optimal CVT whose Voronoi regions are all rescaled copies of the same polytope. Proven only in 2D, Gersho’s conjecture is still open for higher dimensions. One of the main difficulties is that Gersho’s conjecture is a strongly nonlocal, infinite dimensional minimization problem (even in 3D). In this talk we will present some recent results which reduce Gersho’s conjecture to a local, finite dimensional problem in 3D. We will then show how these techniques allow us to analyze qualitative/quantitative properties of ternary polymer systems.

#### Modeling and Analysis of patterns in multi-constituent systems with long range interaction.

Speaker:  Dr. Chong Wang, McMaster University
Date:  Nov 21, 2019
Time:  3:45pm - 4:45pm
Room: DM 409A

Skin pigmentation, animal coats and block copolymers can be considered as multi-constituent inhibitory systems. Exquisitely structured patterns arise as orderly outcomes of the self-organization principle. Analytically, via the sharp interface model, patterns can be studied as nonlocal geometric variational problems. The free energy functional consists of an interface energy and a long range Coulomb-type interaction energy. The admissible class is a collection of Caccioppoli sets with fixed volumes. To overcome the difficulty that the admissible class is not a Hilbert space, we introduce internal variables. Solving the energy functional for stationary sets is recast as a variational problem on a Hilbert space. We prove the existence of a core-shell assembly and the existence of disc assemblies in ternary systems and also a triple-bubble-like stationary solution in a quaternary system. Numerically, via the diffuse interface model, one open question related to the polarity direction of double bubble assemblies is answered. Moreover, it is shown that the average size of bubbles in a single bubble assembly depends on the sum of the minority constituent volumes and the long range interaction coefficients. One further identifies the ranges for volume fractions and the long range interaction coefficients for double bubble assemblies.

#### Algebraic geometry, codes, and post-quantum cryptography

Speaker:  Gretchen Matthews, Virginia Tech
Date:  Nov 13, 2019
Time:  11:45am-12:45pm
Room: DM 409A

How do we store private information? How do we communicate information securely? Answers to these questions are changing as computational capabilities change. Addressing them is vital not only to our national security but also our everyday existence, impacting commerce, healthcare, and the ways in which we interact with one another. Quantum computing poses a threat to current encryption schemes which underpin nearly all digital transactions, thus making a replacement necessary. We share modernizations of McEliece’s 1978 code-based cryptosystems which are based on polynomials and provide robust post-quantum security for classical information. The McEliece cryptosystem utilizes error-correcting codes to keep private information secure, and its effectiveness depends on the properties of the underlying codes. In this talk, we consider the use of algebraic geometric (AG) codes in the McEliece cryptosystem and demonstrate modifications of traditional AG codes that yield superior performance.

#### Dispersive shocks and blow-up

Speaker: Christian Klein, Institut de Mathématiques de Bourgogne, France
Date: Oct 31, 2019
Time:  3:45pm-4:45pm
Room:  DM 409A

#### Active information and some applications

Speaker:   Daniel Diaz, Division of Biostatistics, University of Miami
Date: Oct 24, 2019
Time:  3:45pm-4:45pm
Room:  DM 409A

Active information can be defined as the quantity that is averaged in order to obtain the Kullback-Liebler distance. We introduce the concept, present examples of applications in areas like evolutionary algorithms, mode hunting, and others as time permits.

#### Techniques for Assessing water infrastructure for nonstationary extreme events in the era of climate change.

Speaker:   Jayantha Obeysekera, Department of Earth and Environment, FIU
Date:  Oct 17
Time:  3:45pm-4:45pm
Room:  DM 409A

Statistical and physically based methods have played a fundamental role in designing and assessing water infrastructure such as stormwater drainage systems.   Traditional approaches assume the world is stationary over time. Recent attention to climate change suggests that a new paradigm based on nonstationarity is needed for planning and design.   This presentation will review climate change projections, various statistical techniques that have been developed for modeling nonstationary extreme events, model fitting, estimation of uncertainties, and revisit risk and return period concepts widely used in engineering.   Challenges in applying such techniques in real world situations and the need for using adaptive pathways for dealing with climate change uncertainties will also be discussed.

#### Space based detection of small ground movements using Interferometric Synthetic Aperture Radar (InSAR): Principles, applications, and limitations

Speaker:   Shimon Wdowinski, Department of Earth and Environment, FIU
Date:  Oct 10
Time:  3:45pm-4:45pm
Room:  DM 409A

#### Stochastic Gradient Ascent - My Career in Data Science

Speaker:   Robert Alvarez, Head of Data Science at Podium Education
Date:  Oct 3
Time:  3:45pm-4:45pm
Room:  DM 409A

#### Exploring Climate Time Series In R (Including geographically tagged NetCDF files)

Speaker:   John Tenenholtz, Department of Math & Statistics, FIU
Date:  Sept 26
Time:  3:45pm-4:45pm
Room:  DM 409A

#### On geodesics in Riemannian surfaces with negative curvature

Speaker:  Prof. Jose Manuel Rodriguez Garcia, Univ. Carlos III Madrid
Date:  Aug 29
Time:  3:45pm-4:45pm
Room:  DM 409A

In this work we give a lower bound for the visual Hausdorff dimension of the geodesics escaping through different ends of Riemannian surfaces with pinched negative curvature. This allows us to show that in any Riemannian surface with pinched negative curvature and infinite area there is a large set of geodesics escaping to infinity.

#### Problems and Methods in Environmental Finance

Speaker: Pablo Olivares, Ryerson University, Canada
Date: May 6
Time: 11am-12pm
Room: DM 409A

We review some problems, models and methods that have been proposed to analyze the risk of weather-related variables, such as temperatures and precipitation, and its impact in the environment as well as in related economic sectors such as agriculture, energy, tourism, transportation and local governments.

In order to mitigate these risks, contracts based on the behavior of such variables have been established. We discuss techniques to price them using suitable approximations of the conditional price under realistic stochastic models that include empirical features.

#### On orthogonal polynomials, Hermite-Padé approximants and Riemann-Hilbert problems

Speaker: Sergio Medina
Date: April 18
Time: 3:45pm-4:45pm
Room: DM 409A

In this talk, we will introduce a general formulation of the Hermite-Padé approximation problem which will allow us to show a direct connection among orthogonal polynomials, Hermite-Padé approximants, and Riemann-Hilbert problems.  We will state this connection as general as possible, therefore all the most interesting cases (orthogonal polynomials,  matrix orthogonal polynomials, multiple orthogonal polynomials,  biorthogonal polynomials, among others) can be included in this general formulation.

#### On some extremal problems for polynomials

Speaker: Alex Stokolos, Georgia Southern University
Date: April 11
Time: 3:45pm-4:45pm
Room: DM 409A

In this talk we will discuss some extremal problems for polynomials. Applications to the problems in discrete dynamical systems as well as in the geometric complex analysis will be suggested.

#### Exploring New Version of DIMTEST for Polytomous Data

Speaker: Tan Li, Department of Biostatistics, FIU
Date: March 21
Time: 3:45pm-4:45pm
Room: DM 409A

Item Response Theory (IRT), a latent trait theory, is the major paradigm describing how to model the relationship between examinee ability and the examinee responses to the items on a test. It can be applied to statewide standardized tests, such as SAT and GRE, for purposes including scoring, equating, and scaling. Unidimensionality is a main assumption for IRT. Violating this assumption could seriously bias item and ability parameter estimation. Thus, it is important that the unidimensionality evaluation of tests be efficiently and effectively carried out on a routine basis. While the vast majority of statewide standardized tests contain both dichotomous and polytomous items, much of the work in dimensionality assessment has focused on the case of dichotomous item exams. This presentation will introduce Poly-NEWDIM, a nonparametric hypothesis testing procedure for dimensionality assessments of polytomous exams. It is demonstrated to have closer to nominal Type I error control and better power than the currently existing method.

#### Dynamics of complex singularities and integrability of surface motion

March 7, 3:45-4:45pm, DM 409A

Speaker: Pavel Lushnikov, University of New Mexico
Date: March 7
Time: 3:45pm-4:45pm
Room: DM 409A

A motion of fluid's free surface is considered in two dimensional (2D) geometry. A time-dependent conformal transformation maps a fluid domain into the lower complex half-plane of a new spatial variable. The fluid dynamics is fully characterized by the complex singularities in the upper complex half-plane of the conformal map and the complex velocity. Both a single ideal fluid dynamics (corresponds e.g. to oceanic waves dynamics) and a dynamics of superfluid Helium 4 with two fluid components are considered. A superfluid Helium case is shown to be completely integrable for the zero gravity and surface tension limit with the exact reduction to the Laplace growth equation which is completely integrable through the connection to the dispersionless limit of the integrable Toda hierarchy and existence of the infinite set of complex pole solutions. A single fluid case with nonzero gravity and surface tension turns more complicated with the infinite set of new moving poles solutions found which are however unavoidably coupled with the emerging moving branch points in the upper half-plane. Residues of poles are the constants of motion. These constants commute with each other in the sense of underlying non-canonical Hamiltonian dynamics. It suggests that the existence of these extra constants of motion provides an argument in support of the conjecture of complete Hamiltonian integrability of 2D free surface hydrodynamics.

#### Calculus Yesterday, Today, and Tomorrow

Speaker: Deb Hughes Hallett,  University of Arizona Harvard Kennedy School
Date: March 4
Time: 2pm-3pm
Room: DM 409A

Has the teaching of calculus changed over the past decades? If so, how and why? What are the challenges in teaching calculus today?  Can we anticipate future challenges? This talk will suggest answers to these questions and discuss how mathematics departments can best prepare our current and future students.

View recorded lecture

#### On Markov statistical solutions of differential equations

Speaker: Lev Kapitanski, University of Miami
Date: Feb. 21
Time: 3:45pm-4:45pm
Room: DM 409A

In this talk I will describe different types of statistical solutions (in particular, Hopf, Foias, and Fursikov solutions), explain what Markov solutions are, discuss an abstract theorem on their existence, and give a few examples. The talk is based on joint work with Jorge E. Cardona.

#### How stochastic shocks influence adetermistic life

Speaker: Annie Millet, University Paris 1
Date: Feb. 7
Time: 3:45pm-4:45pm
Room: DM 409A

I will present some results on parabolic or dispersive nonlinear PDEs subject to a random perturbation. This « noise » models the sum of many infinitesimal shocks in the environment. Besides well posedness, some properties of the solution will be discussed, such as discretization schemes, concentration of the distribution when the intensity of the noise approaches 0, long time behaviour.

#### Global Well-Posedness and Sobolev Bounds for Non-Focusing Schrodinger Equations on Mixed Domains

Speaker: Nathan Totz, University of Miami
Date: Jan. 31
Time: 3:45pm-4:45pm
Room: DM 409A

We consider the long time well-posedness of the Cauchy problem with large Sobolev data for a class of nonlinear Schrodinger equations (NLS) on mixed flat/periodic domains of spatial dimension $d \geq 3$, and with power nonlinearities of arbitrary odd degree. This class of equations includes a family of energy supercritical defocusing NLS equations. We argue by contradiction that, if certain scaling-subcritical Sobolev norms of a solution increases faster than a certain threshold of polynomial growth, we can directly construct a slight perturbation of the solution that grows slower than this polynomial growth rate, violating classical stability results. In particular, this establishes unconditional global well-posedness on all subcritical Sobolev norms. The perturbed NLS solution at the core of the argument is constructed as a modulational limit of a carefully constructed artificial evolution equation.

#### Relative entropy of compressible model for fluid mixtures

Speaker: Xiaokai Huo, KAUST
Date: Jan. 10
Time: 3:45pm-4:45pm
Room: DM 409A

The relative entropy method was first developed in the context of hyperbolic system of conservation laws. It provides a measure of the difference between solutions. In this talk, I will show the application of this method in studying the relaxation limit of a multi-species Euler-Korteweg system. I will first show the formal derivation of the limit equations via asymptotic analysis. Then I will derive a relative entropy inequality for the difference between weak solutions to the original system and strong solutions to the approximate system. Finally, I will present the nonlinear estimates using the relative entropy methods and prove the convergence theorem. The relative entropy method provides a nature nonlinear estimate and is the key to obtaining the convergence result.

• 2018

#### Speaker: Ryan Integlia, Review of efforts towards bioinspired design and strategy to integrated networked wearables, gaming and robotic systems

Nov. 29, 3:45pm - 4:45pm , DM 110

Prof. Ryan Integlia, Florida Polytechnic University

This presentation will cover the current and future developments of a complex, extensible, intelligent robotics platform.  The intended use of the platform is for developing bio-inspired swarming robots that are able to gauge their surroundings and act accordingly.  The system is based on Boids, a simple flocking algorithm. The primary focus of this presentation will be the prior art and development of the platform, as well as the  broad concept of bio-mimicry).

Prof. Integlia's student Kendon Ricketts will give a follow-up talk on Nov. 30, DM 409 at 9:45am.

#### Speaker: Roberto Triggiani

Nov. 1, 3:45pm - 4:45pm, DM 409A

University of Memphis

#### Mathematical Modeling of Lung Cancer Screening Studies

Oct. 25, 3:45pm - 4:45pm, DM 409A

#### The Angle Function

Oct. 16, 2:00pm - 3:00pm, GC 271A

Speaker: Phillippe Rukimbira

#### Crowdmark

Oct. 5, 9:50pm - 10:50pm, DM 409A

We will have discussion and presentation about online grading system Crowdmark at the Applied Math seminar.

#### Nonlinear phenomena in analysis and PDEs

Oct. 4, 3:30pm - 4:30pm, DM 409A

Svetlana Roudenko will give an informal talk at the graduate students seminar on her research on nonlinear phenomena in analysis and PDE.

#### Adaptive Tracking and Parameter Identification

Feb 27, 11:00am - 12:00pm, GC 285

This talk will summarize the speaker's work on adaptive tracking and parameter identification, including an application to curve tracking problems in robotics. The talk will be understandable to those familiar with the basic theory of ordinary differential equations.

• 2017

#### Tom Wright "Carmichael Numbers: Elliptic and Arithmetical"

Dec. 11, 2:30pm - 3:30pm, DM 409A

Carmichael numbers are numbers which satisfy a certain test for primality but are nevertheless not prime. In this talk, we discuss several new results on Carmichael numbers.

#### Anxiety, STEM Identity and Persistence in Mathematics Courses

Dec. 5, 4:00pm - 5:00pm, WC 130

Speaker: Edgar Fuller, West Virginia University / In this talk we will discuss the results of this study and give an overview of the anxiety levels observed among these students, the personality traits, self-efficacy levels and their sense of STEM belonging. We well describe a peer-mentoring intervention and its impact on student success.

#### Dept meeting on precalculus and calculus

Sep. 26, 3:30pm - 5:00pm, PC 310

#### Music, Time-Frequency Shifts, and Linear Independence

May 15, 3:30pm - 4:30pm, Christopher Heil Georgia Tech

We will discuss time-frequency representations, which are a type of local Fourier representation of signals.

#### Conference in Statistical Methods and Mentoring

Apr. 21, 10:00am - 5:00pm, CBC 142

#### Long Time Behavior of Solutions to the Generalized Hartree Equation

Apr. 11, 3:30pm - 4:30pm, DM 100

In this talk we present small data theory, dichotomy for scattering versus blow-up, and criteria for solutions that blow-up in finite time with an emphasis on the method of concentration - compactness.

#### Topological and fractal properties of non-integer base expansions

Mar. 30, 3:30pm - 4:30pm, DM 100

Here we mostly discuss the uniqueness of expansions. The talk is based on joint research with P. Erdős, I. Joó, P. Loreti, A. Pethő, M. Pedicini, M. de Vries, A.C. Lai, M. Baatz, S. Akiyama, D. Kong and W. Li.

#### Non-convex iterative L1 methods for sparse/low-rank reconstruction problems

Mar. 29, 3:40pm - 4:40pm, DM 110

Speaker: Dr. Penghang Yin [UCLA] / In this talk, we introduce a general algorithmic framework, based on the difference of convex functions algorithm, for minimizing a class of non-convex sparse metrics.

#### The Difference of L1 and L2 for Compressive Sensing and Image Processing

Feb. 13, 2:00pm - 3:00pm, DM 110

In this talk, I will present a novel non-convex approach, which is to minimize the difference of L1 and L2 norms (L1-L2) in order to promote sparsity. In addition to theoretical aspects of the L1-L2 approach, I will discuss two minimization algorithms.

#### Study of the chaotic vibration of the 2D non-strictly hyperbolic equation

Feb. 10, 2:00pm - 3:00pm, DM 100

Prof. Jing Tian from University of South Florida / In this talk, I will mainly discuss the chaotic vibration phenomenon of the 2D non-strictly hyperbolic equation due to an energy-injection boundary condition and a distributed self-regulation boundary condition.

#### Systems generated from the iterative actions of operators

Feb. 2, 3:30pm - 4:30pm, DM 144

Prof. Akram Aldroubi,. Vanderbilt University / In this talk, we present some of the recent developments concerning frames and Bessel systems generated by iterations of the form {A^ng: g in G,, n=0,1,2,...} where A is a bounded linear operator on a separable complex Hilbert space H and G is a countable set of vectors in H .

#### The Calabi-Yau problem on the Kodaira-Thurston manifold

Jan. 3, 4:30pm - 5:30 pm. DM 409A

• 2016

#### Decentralized consensus optimization on networks with delayed and stochastic gradients

Nov. 10, 3:30pm - 4:30pm, DM 110

Prof. Xiaojing Ye from Georgia State Univ. / In this talk, we focus on a decentralized consensus algorithm by taking the delays of gradients into consideration.

#### Seminar talk: Ants and Bees: Some properties of cellular automata

Oct. 21, 2:00pm - 3:00pm, PC 426

David Gillman Assistant Professor of Computer Science New College of Florida / I will show a computer visualization of the ant and the bee that displays some of their recurring and limiting behaviors. I will survey what is known and what is conjectured about these behaviors.

#### Big Medical Data in Brain Imaging

Sep. 22, 3:30pm - 4:30pm, DM 110

Speaker: Dr. Ruogu Fang, School of Computing and Information Sciences at FIU / In this talk, I will present the big picture of the challenges faced by the world and the US healthcare system in the age of big medical data, and opportunities open for research, and our advances on using the big medical data for more accurate and safer medical diagnosis.

#### Speaker: Chris Rasmussen, San Diego State University

Apr. 6, 11:00am - 12:00pm, PG6 room 115

Title: Coordinating Analyses of Individual and Collective Mathematical Progress: A Case of Creating and Using Euler's Method in Differential Equations

#### On the geometry of random lemniscates

Mar. 30, 1:30pm - 2:30pm, GC 283A

Prof. Erik Lundberg, from Florida Atlantic University, will give a colloquium talk.

#### A model of arterial plaque cap development and degradation

Mar. 24, 4:00pm - 5:00pm, DM 194

Professor Jon Bell, U Maryland, Baltimore County / We introduce a model involving some of these dynamic processes, prove some theoretical results, do some simulations, and examine the implications of the model results.

#### Geometric structures, Gromov norm and Kodaira dimensions

Mar. 22, 3:30pm - 4:30pm, GL 166

Professor Weiyi Zhang, University of Warwick / In this talk, we will define the Kodaira dimension for 3-manifolds through Thurston’s eight geometries.

#### Asymptotically Conical Calabi-Yau manifolds

Mar. 3, 3:30pm - 4:40pm, DM 193

Dr. Ronan Conlon from Université du Québec a Montréal will speak. / He will describe how, in certain instances, one is able to determine all AC Calabi-Yau manifolds modelled on some given Ricci-flat Kähler cone. This is joint work with Hans-Joachim Hein.

#### Dr. Qi Han from Worcester Polytechnic Institute

Feb. 22, 3:00pm - 4:00pm, PC 428

Dr. Qi Han from Worcester Polytechnic Institute will speak. The title is Harmonic Steklov Eigenvalue Problems, Compact Embedding of Sobolev Spaces, and Applications.

#### Speaker: Dr. Xu Zhang , Purdue University

Feb. 12, 3:30pm - 4:30pm, DM 193

Immersed Finite Element Methods for Interface Problems. / We will present challenges of classical IFE methods, and introduce some recent advances in designing more accurate and robust IFE schemes. Mathematical convergence theories and some numerical experiments will be presented. At last, we will demonstrate how IFE methods can be applied to more complicated interface model problems.

#### Dr. Geng Chen: Large solutions of compressible Euler equations

Feb. 4, 3:30pm - 4:30pm, DM 193

In this talk, I will discuss some recent exciting progresses in this direction. In first part of this talk, I will discuss our complete resolution of shock formation problem, which extends the celebrated work of Peter Lax on small solutions in 1964.

#### Dr. Yanqiu Guo from Texas A&M University will speak

Feb. 2, 3:30pm - 4:30pm, DM 193

Title: Competing Forces in Nonlinear Partial Differential Equations / I will discuss several physical models and explain the competition of damping and sources in nonlinear wave equations, the interaction of dispersion and nonlinearity in nonlinear dispersive equations, as well as the relation of diffusion and convection in Navier-Stokes equations.

#### Speaker: Dr. Walter Carballosa

Jan. 26, 4:00pm - 5:00pm, TBA

Dr. Walter Carballosa, (MDC) / Title: On the Gromov hyberbolicity of planar graphs / In this work we obtain criteria which allow us to decide for a large class of graphs whether they are hyperbolic or not.

#### Talk by Professor Gideon Maschler, Clark University

Jan. 12, 3:30pm - 4:30pm, DM 409A

Title: Distinguished metrics in conformal classes / We first briefly describe the case where the first of the two metrics is Einstein, where a fairly complete description can be given, even globally. We then turn to other first metric types, such as a gradient Ricci soliton, and, if time permits, versions of the Einstein and soliton conditions that are adapted to warped product constructions.

• 2015

#### Speaker: Dr. Antonio Lerario, SISSA (Trieste) and FAU

Nov. 19, 3:30pm - 4:30pm, GL 132

Title: "Statistics on Hilbert's Sixteenth Problem" / In this talk I will present a probabilistic approach to this problem, discussing new exciting questions related to the topology of random hypersurfaces. (This is joint work with E. Lundberg)

#### Speaker: Dr. Sergio Medina, MDC

Nov. 12, 3:30pm - 4:30pm, GL 132

Title: On the convergence of Hermite-Padé approximants / In this talk we will present some recent results about the uniform convergence of these Hermite-Padé approximants and one application related with the solutions of the Degasperis-Procesi differential equations.

#### General monotonicity and interpolation of operators

Nov. 5, 3:30pm - 4:30pm, GL 132

Title: "General monotonicity and interpolation of operators" / Using interpolation properties of cones of general monotone functions, we prove the equivalence of the L(p,q) norms of such functions and their Fourier transforms.

#### Divergence and Entropy inequalities for log concave functions

Oct. 29, 3:30pm - 4:30pm, DM 190

Dr. Umut Caglar, FIU / In this talk we obtain analytic versions of several geometric invariants and inequalities.

#### Otávio Bueno: What Does a Mathematical Proof Really Prove?

Apr. 9, 3:30pm - 4:45pm, SIPA 103

#### Seminar talk: Prof. Dmitry Khavinson from USF

Apr. 8, 2:00pm - 3:00pm, DM 409

We shall discuss questions in the unified light of analytic continuation of solutions to linear analytic pde. The talk will be accessible to undergraduate and graduate students majoring in math, physics and engineering.

#### Solvability near the characteristic set for a class of first order linear partial differential operators

Mar. 5, 3:30pm - 4:30pm, GL 165

Paulo Dattori, (visiting professor at FIU) / n this talk we will address to the following problem: Given a smooth function f in a neighborhood of K, is there a smooth (or else continuous) function u solution of Pu=f in a neighborhood of K?

#### Scattering Resonances for Photonic Structures and Schrodinger Operators

Feb. 12, 3:30pm - 4:30pm, DM 100

Dr. Junshan Lin from the Department of Mathematics and Statistics / In this talk, I will present recent studies on the scattering resonances for photonic structures and Schrodinger operators.

#### Prof. Eli Lifljand, (Bar-Ilam Univ)

Jan. 29, 3:30pm - 4:30pm, DM 409A

Fourier Transfrom versus Hilbert Transform / We present several results in which the interplay between the Fourier transform and the Hilbert transform is of special form and importance.

#### Prof. Sergei Avdonin, Univ. of Alaska

Jan. 8, 3:30pm - 4:30pm, TBA

Spectral and Dynamical Inverse Boundary Problems / In this talk we describe the main ideas of this method, as well as its main features, such as locality.

• 2014

#### Speaker: Prof. Olivares, Ryerson University (Toronto)

Dec. 11, 3:30pm - 4:30pm, DM 409A

Pricing Basket European Contracts under Discontinuous Models by Polynomial Approximations (joint work with Alvarez, Klyueva and Villamor) / I present some results about pricing basket European contracts such as spreads and exchange options considering approximation techniques based on Bernstein, Chebyshev and Taylor polynomials.

#### Using shape-based methods to analyze biological data

Dec. 2, 3:30pm - 4:30pm, SIPA 103

Speaker: Valerie Hower from UM / I will introduce the basic ideas of TDA and give some examples of its use in biology. I will also include my own work using shape-based methods to analyze next generation sequencing data.

#### Geometry Seminar: The Kahler-Ricci flow and its singularities.

Dec. 1, 11:00am - 12:00pm, DM 144

Speaker: Professor Valentino Tosatti from Northwestern University / I will give an introduction to the study of Ricci flow on compact Kahler manifolds, and explain how its behavior reflects the structure of the complex manifold.

#### Seminar talk : Inverse problem for discretized heat equation

Nov. 25, 3:30pm - 4:30pm, SIPA 103

Speaker: Julian Edward / We study a discretized version of this problem, using the Boundary Control Method.

#### Spectral Tetris and Construction of Frames

Nov. 20, 3:30pm - 4:30pm, SIPA 100

Prof. Keri Kornelson Univ. Oklahoma / In this talk, we will discuss the construction of tailor-made frames in finite dimensions.

#### Seminar: "Proofs in the digital world"

Oct. 10, 2:00pm - 3:30pm, ECS 241

Prof Silvio Micali, Comp.Sci. and A.I. Lab, MIT Sponsored by the C.S.Dept.

#### Student-Faculty Soccer Game

Sep. 28, 5:00pm - 7:00pm, Kendall Soccer Park

This up coming Sunday the Math Club will be hosting another Student-Faculty Soccer Game for this year due to significant enthusiasm from both sides.

#### Seminar: Tom Leness "SO(3) monopoles and superconformal simple type"

Sep. 18, 3:30pm - 4:30pm, GL 100A

In this talk, I hope to explain how the SO(3) monopole cobordism formula implies the truth of this conjecture.

#### Dept meeting with the Dean

Sep. 9, 3:30pm - 4:30pm, SIPA 103

Not to be confused with our 9/4 meeting, this one is with our new Dean.

#### Geometry Seminar: M.Parton

Aug. 22, 4:00pm - 5:00pm, DM 409A

Title: Spin(9) and octonionic geometry. / Starting from the description of the Lie group Spin(9) as generated by 9 involutions in SO(16), I will sketch out how it is involved in the existence of "many" never-vanishing vector fields on spheres, and in the construction of a "matryoshka" of differential forms.

#### Departmental meeting

Apr. 28, 3:00pm - 4:00pm, DM 409A

#### Seminar: Prof. E. Laeng, Politecnico di Milano (Italy)

Apr. 24, 3:00pm - 4:00pm, DM 409A

Title: L^p norms of the Hilbert transform of a characteristic function and related topics / We give explicit formulae for the L^p norms of the Hilbert transform of the characteristic function of a measurable subset of the line of finite Lebesgue measure.

#### Jeremiah Hower, FIU: Arithmetic Surfaces and their Graphs

Apr. 17, 3:30pm - 4:30pm, SIPA 100

We will discuss their connection to reducing a system of equations (with integer coefficients) modulo a prime. A new result relating the eigenvalues of a (generalized) Laplacian to the Smith Normal Form will be given.

#### CAS Faculty Online Symposium 2014

Apr. 11, 8:30am - 3:30pm, MARC Pavilion

Come and join us on our annual CAS Faculty Online Symposium with are keynote speaker Allan Gyorke from the University of Miami.

#### Speaker: Prof. Mario Milman, FAU

Apr. 7, 1:00pm - 2:00pm, RB 130

Title: as a way of introduction: some results in analysis and probability / I will discuss some recent results on Sobolev inequalities and optimization and tell some anecdotes on how they came about.

#### Dr. D. Gary Harlow: Lehigh University

Apr. 4, 3:30pm - 4:30pm, DM 110

The talk should be suitable for students and faculty in both statistics and engineering units.

#### Colloquium Speaker: Xiaoming Wang, Florida State University

Mar. 31, 3:00pm - 4:00pm, RB 130

We discuss the scaling of the long time averaged rate of heat transport in the vertical direction, quantified as the Nusselt number, within the Rayleigh-Benard model for convection.

#### Speaker: Prof. Luz de Teresa

Mar. 4, 3:45pm - 4:45pm, DM 409A

The title is "Condensation index and controllability of parabolic systems" / In this talk we will give survey of the controllability results of coupled parabolic equations when exerting the control on the boundary.

#### Department Meeting

Feb. 27, 3:30pm - 4:30pm, DM 409A

The meeting will be about our Bachelor Degree and Teachers Certificate.

#### Seminar talk by Dr. A. Dochtermann

Feb. 20, 3:30pm - 4:30pm, DM 409A

Title: Edge ideals, resolutions, and spaces of graph homomorphisms / A common theme in combinatorics is to take a discrete object and associate to it some algebraic or topological structure. The idea is that one can then use tools from one discipline(s) to answer questions in the other.

#### Seminar talk: Prof Alex Iosevich

Feb. 18, 3:45pm - 4:45pm, SIPA 103

Title: Geometric configurations in Euclidean space and discrete settings / We shall discuss the distribution of finite point configurations in Euclidean space and vector spaces over finite fields.

#### Talk by Alex Stokolos, "Bellman Functions - be perfect at every step"

Feb. 6, 3:30pm - 4:30pm, DM 409A

In the talk I will illustrate basic steps of the method on examples of classical Holder inequality and estimates of dyadic Hardy-Littlewood maximal function.

• 2013

#### Prof C Gal: Biological aggregation in nonlocal models

Nov. 5, 3:30pm - 4:30pm, DM 409A

I wish to discuss recent developments concerning the long term behavior in terms of (possibly finite-dimensional) global attractors and convergence to a single equilibrium, as time goes to infinity, of solutions to a continuum model for biological aggregations. The model is the aggregation equation with both degenerate and non-degenerate diffusion in which individuals experience long-range social attraction and short range dispersal.

#### Santiago Simanca, Univ. of Miami: The vibrations of an unassembled violin plate

Oct. 29, 3:30pm - 4:30pm, DM 409A

We model the elastic properties of wood by treating it as a body that satisfies the generalized Hooke law, and so its stress tensor is a linear function of its strain. It has three mutually orthogonal planes of symmetries at each point, the lines parallel to the fiber grains, the radial axis normal to the growth rings, and the tangential axis.

#### Molecular Pattern Formation, Networks, and Graph Theory Can Cause You to Lose Your Mind

Oct. 15, 3:30pm - 4:30pm, DM 409A

Catastrophic neurological diseases such as Alzheimer’s and Parkinsons’s occur in the presence of multi-protein aggregates with a specific pattern of hydrogen bonds. The same proteins originate in molecular configurations that are innocuous. These proteins undergo a major structural conversion while converting to the toxic amyloid aggregates. During the structural conversion process, the global H-bond network undergoes a transformation. We propose that the transformation of the H-bond network is the dominant factor in controlling the dynamics of the structural conversion and aggregation. Therefore, determining the details of the transformation of the H-bond network will provide insight on the underlying molecular mechanism of amyloid fibril formation.

#### Seminar talk by Prof Julian Edward. "Determining aquifer transmissivity..."

Oct. 8, 3:30pm - 4:30pm, DM 409A

A standard way of determining aquifer transmissivity is using a slug test together with a mathematical model using Darcy's law. This model is briefly reviewed, and then an alternative model using Forcheimer's equation is presented. Problems involving numerical and closed form solutions are discussed. This is a preliminary report.

#### Professor Pablo Olivares, Ryerson University, Canada: Pricing Multidimensional Derivatives under Processes with Conditional Independent Increments

May 8, 3:30pm - 4:30pm, DM 409A

We discuss some ideas and preliminary results about pricing multidimensional financial contracts such as basket and spread options considering the dynamic of the underlying instruments driven by a variety of stochastic models, from multidimensional Black-Scholes with constant correlation to Levy models with finite and infinity activity, to stochastic covariance models with Levy background noise. Pricing methods such as Fast Fourier Transform and several approximated closed-form techniques will be considered, as well as some fitting methods using minimum distance estimations with applications to the modeling of oil prices.

#### Yuan Yuan, Johns Hopkins University

April 18, 3:30pm - 4:30pm, DM 409A

Local holomorphic isometries were systematically studied in 50's by Calabi and recently number theorists applied the geometry and analysis for local holomorphic maps between bounded symmetric domains to attack the problem in number theory, which also motivates our study of such questions. I will describe the main theorems on the global extension and the rigidity for local holomorphic isometries between Hermitian symmetric spaces and explain the relation with CR geometry and proper holomorphic mappings between balls.

#### Anna Fino, Univ di Torino: Symplectic geometry and special Hermitian structures

April 11, 3:30pm - 4:30pm, DM 409A

Symplectic forms taming complex structures on compact manifolds are strictly related to a special type of Hermitian metrics, known in the literature as "strong Kaehler with torsion" metrics. I will present general results on "strong Kaehler with torsion" metrics and their link with symplectic geometry. Moreover, I will show for certain 4 -dimensional non-Kaehler symplectic 4 -manifolds some recent results about the Calabi-Yau equation in the context of symplectic geometry.

#### Ramesh Sharma, University of New Haven: Ricci and Yamabe Solitons In Contact Riemannian Geometry

March 21, 3:30pm - 4:30pm, DM 409A

This talk will begin with a brief introduction to Ricci and Yamabe solitons, and then present a survey of results on the characterization and classification of Ricci and Yamabe solitons as Riemannian metrics associated to a contact structure, in particular Sasakian structures. It would conclude with some interesting open questions.

#### Augustin Banyaga, Penn State: Non-existence of certain Einstein metrics on some symplectic manifolds

Feb. 15, 1:30pm - 2:30pm, AHC3 205

We exhibit a necessary and sufficient condition for a symplectic manifold $(M, \omega)$ to admit an $\omega$- compatible Einstein metric. This research was motivated by the Goldberg conjecture asserting that a compact symplectic manifold $(M,\omega)$ with an $\omega$- compatible Einstein metric is Kaehler. This is a joint work with F. Massamba.

Biosketch: Augustin Banyaga is a Professor of Mathematics at Penn State University, University Park. His research areas are in Symplectic, Contact Geometry and Topology, and Morse Theory ( Morse Homology, Morse-Bott homology). Lately he has worked on the foundations of the $C^0$ symplectic Topology and the Hofer Geometry. Augustin Banyaga is a Fellow of the African Academy of Sciences

#### Prof. Juan Carlos Osorio: Relations among Stiffness coefficients of hexahedral of 8-noded finite elements

Feb. 13, 3:30pm - 4:30pm, DM 409A

Computing coefficients in stiffness matrices of finite element analysis in computational mechanics is time consuming, especially in large non-linear dynamic problems involving large meshes. Thus, any improvement in computational procedures to reduce the integration CPU time is welcomed. In this work, we suggest an efficient approach based on linear equations to describe the cross-relations among the element's shape-functions derivatives to compute three coefficients of the nodal stiffness submatrix as a function of other coefficients previously computed. The coefficients can relate different degrees of freedom at a given node in the element. They are used to evaluate other coefficients inside the same nodal submatrix. These equations give a Improvements of 28% of CPU time are obtained when the approach is applied to three dimensional discretizations with eight-node brick finite elements.

#### Isoparametric functions and harmonic unit vector fields in K-contact Geometry

Jan. 24, 3:30pm - 4:30pm, DM 409A

Phillippe Rukimbira will speak on Isoparametric functions and harmonic unit vector fields in K-contact Geometry Abstract: I will present some examples of harmonic unit vector fields as normalized gradients of isoparametric functions in a K-contact geometry setting.

• 2012

#### Prof. V. Tosatti, Northwestern U.: The Chern-Ricci Flow

Dec. 20, 2:00pm - 3:00pm, DM 409A

I will discuss the evolution of a Hermitian metric on a compact complex manifold by its Chern-Ricci curvature. This is an evolution equation which coincides with the Ricci flow if the initial metric is Kahler, and was first studied by M.Gill. I will describe the maximal existence time for the flow in terms of the initial data, and then discuss the behavior of the flow on (mostly non-Kahler) complex surfaces as one approaches the maximal existence time. This is joint work with Ben Weinkove and partly with Xiaokui Yang.

#### Bao Qin Li: On L-functions determined by their zeros

Dec. 4, 4:00pm - 5:00pm, GL 137

L-functions are Dirichlet series with the Riemann zeta function as the prototype and most L-functions in number theory share certain common properties. We will consider how L-functions in the Selberg class are determined by their zeros and discuss some recent results in this direction.

#### Sergei Avdonin, University of Tennessee at Chattanooga: Riesz Bases of Exponentials and their Applications

Nov. 15, 4:00pm - 5:00pm, GL 137

We present some classical and recent results concerning properties of exponential families and vector exponential families. Several applications to control theory and signal processing will also be discussed.

#### Prof. Der-Chen Chang, Georgetown University: Heat kernels of a class of degenerate elliptic operators

Nov. 6, 4:00pm - 5:00pm, GL 137

In this talk, we discuss the geometry induced by a class of second-order subelliptic operators. This class contains degenerate elliptic and hypoelliptic operators (such as the Grushin operator and the Baouendi-Goulaouic operator). Given any two points in the space, the number of geodesics and the lengths of those geodesics are calculated. We find modified complex action functions and show that the critical values of these functions will recover the lengths of the corresponding geodesics. We also find the volume elements by solving transport equations. Then heat kernels for these operators are obtained.

#### Camilo Montoya, FIU: Polarizations of real hypersurfaces in C^n

Oct. 16, 4:00pm - 5:00pm, GL 137

Segre varieties and their intersections, known as polarizations, are particular biholomorphic invariants attached to real-analytic hypersurfaces in Cn. These invariants are studied and used to construct a family of real hypersurfaces in n-dimensional complex space that have a large family of analytic sets with nontrivial polarizations. A result that effectively classifies all hypersurfaces with such family of analytic sets and their polarizations is proven.

#### M. Lejmi talk, part 2

Oct. 1, 11:00am - 12:00pm, DM 409A

Our visitor M. Lejmi will continue his colloquium talk from Tuesday on the Geometry seminar Monday, 10/01 at 11am in DM409. The title and the abstract are below. Geo Title: Deformations of non-integrable Hermitian-Einstein metrics. Abstract: Previously, we studied deformations of extremal almost-kahler metrics starting from an extremal (integrable) kahler metric. In this talk, we explore deformations of these metrics but starting from (not integrable) extremal almost-kahler metric.

#### Prof M. Lejmi

Sept. 25, 4:00pm - 5:00pm, GL 137

Calabi defined the notion of extremal Kähler metrics in order to widen the problem of existence of Kähler Einstein metrics. For instance, the blow up of CP^2 at one point admits no Kähler metrics with constant scalar curvature but it does admit extremal Kähler metrics as shown by Calabi. Moreover, Calabi proved that the existence of extremal Kähler metrics imposes a certain decomposition of the Lie algebra of the automorphism group of the complex manifold.

I don't think that the talk will be really student-friendly since it needs some background from differential geometry. But I can do my best to define all the notions used in this talk.

• 2011

#### Dr. Tien-Yian Li, University Distinguished Professor, Michigan State University: The Story about Chaos

Nov. 18, 2:00pm - 3:00pm, AHC3 205

As a co-author of the seminal article “Period three implies chaos” in chaos theory, I would like to tell, in this talk, some interesting stories I personally encountered over the years in this area.

#### Ciprian Gal: On quasilinear elliptic equations with fully nonlinear boundary conditions

Nov. 1, 3:30pm - 4:30m, DM 409A

We consider nonlinear elliptic partial differential equations subject to fully nonlinear boundary conditions involving boundary operators of the same order as the bulk operators. We discuss issues such as existence of bounded solutions and regularity. We illustrate the application of our results to a class of uniformly elliptic equations that occur in the theory of phase transitions of different materials, and certain elliptic systems associated with climate problems, which describe the evolution of atmospheric sea-level temperatures for relatively long time scales.

#### William Yslas Vélez, U. Ariz.: Mathematics Changed My Life [Math Club]

Sept. 29, 3:30pm - 4:30pm, AHC3 110

Our special guest speaker William Yslas Vélez from the Math department of University of Arizona will be giving a presentation entitled "Mathematics Changed My Life" in AHC 3110 . This will be held Thursday September 29th, 3:30-4:30, in place of our student colloquium for that week.

#### Prof. William Yslas Velez, U. Ariz.

Sept. 29, 9:30am - 10:30am, GC 283A

Next Thursday and Friday we will be visited by Prof. William Yslas Velez, a math professor from University of Arizona. Recently he has become active in the recruitment of Math majors, and his department has in the past several years doubled their number of majors - they now have 640. He will be addressing our department about his recruitment efforts.

#### Zhijian Wu, Prof. and Chairperson at University of Alabama: Optimal Strategy for Certain Hedging Problem

Aug. 16, 3:30pm - 4:30pm, DM 409A

Under the constraint of terminal risk, we search for an optimal deterministic strategy to reduce the running risk in hedging a long-term commitment with short-term futures contracts. An explicit solution is given if the underlying stock follows the simple stochastic differential equation: $dS_t =mu dt + sigma dB_t$, where $B_t$ is the standard Brownian motion. Our result generalizes the result by G. Larcher and G. Leobacher, and we also provide a solution to the utility optimization problem posed by them.

#### Anca Vaceruscu, Stanford Univ.: Nonlinear Filtering and Parameter Estimation for an Affine Jump Diffusion Process

April 28, 3:30pm - 4:30pm, DM 409A

I consider a nonlinear ﬁltering problem for the generalized Hawkes process, with applications to portfolio credit risk. The investors in the market have access to the credit history of ﬁrms with correlated default risk, but the observations of default times are only available at ﬁxed time intervals. The intensity driving the default counting process is exposed to an unobservable risk factor in the market, but also reacts to a jump in the counting process itself. Thus, a default of a name in the portfolio directly impacts the survival rate of the remaining ﬁrms. I will present some of the properties of the non-linear ﬁlter constructed for this hidden Markov model in discrete time, and its sensitivity with respect to the parameters of the model. I will also address the estimation of parameters in this context, and discuss the implementation of the Expectation Maximization Algorithm for this affine jump diffusion model in an incomplete information set-up.

#### Xiaosheng Li: Inverse Boundary Value Problems in a Slab

April 14, 3:30pm, DM 409A

Inverse boundary value problems arise when one tries to recover internal parameters of a medium from data obtained by boundary measurements. In many of these problems the physical situation is modeled by partial differential equations. The goal is to determine the coefficients of the equations from some measurements of the solutions on the boundary. In this work we consider the inverse problems for Schroedinger equations with Yang-Mills potentials in the domain of infinite slab type. We prove that the potentials can be determined uniquely up to a gauge equivalent class, assuming that only partial measurements are known on the boundary hyperplanes.

#### Lotfi Hermi, Univ. of Arizona: Max-to-Mean Ratio Bounds for the Fundamental Eigenfunction of the Dirichlet Laplacian

March 31, 3:30pm - 4:30pm, DM 409A

Abstract: Max-to-Mean ratio for the fundamental eigenfunction of the Dirichlet Laplacian was developed by Payne-Stakgold, and Payne-Rayner in the early 1970s in the context of shape optimization, with applications in mind. It is a means of gauging various norms of this eigenfunction, and falls in a class known as  "reverse Holder inequalities''. A body of literature has developed around this concept and is now part of core results in Schwarz symmetrization. We review some of its salient features and prove some new results for wedge-like membranes. This is joint work with N. Gamara and A. Hasnaoui (University of Tunis, El-Manar).

#### Prof. Tedi Draghici: On the J-anti-invariant cohomology of almost complex 4-manifolds

March 24, 3:30pm - 4:30pm, DM 409A

We will present some results about the dimension of the space of closed, J-anti-invariant 2-forms of a compact, 4-dimensional almost complex manifold (M,J).

#### Kai Huang: Instant System Availability

March 3, 3:30pm - 4:30pm, DM 409A

In this talk, I will present joint work with Prof. Jie Mi on the instant availability A(t) of a repairable system through integral equation. We will prove some properties of system availability, Numerical algorithm for computing A(t) is proposed. Examples show high accuracy and efficiency of this algorithm.

#### Alex Iosevich

Feb. 24, 3:30pm - 4:30pm, DM 409A

The classical regular value theorem says that if f: X -> Y is an immersion, where X,Y are smooth manifolds of dimension n,m , n>m , respectively, then the set {x in X: f(x)=y } is either empty or is an n-m dimensional sub-manifold of X . We shall see that a suitable analog of this result is available if a manifold X is replaced by a set of sufficiently large Hausdorff dimension and the function f satisfies a "rotational curvature" condition. Regularity of generalized Radon transforms plays a key role. Sharpness results are based on an interplay between ideas from discrete geometry and number theory.

#### Prof. Bo YU, Dalian Institute of Technology (China): Hybrid Divide-and-Conquer Methods for Solving Polynomial Systems

Feb. 11, 1:00pm - 2:00pm, DM 409A

In this talk, a brief introduction of some hybrid divide-and-conquer methods for solving polynomial systems will be given. At first, for polynomial systems derived from mixed trigonometric polynomial systems, a hybrid homotopy and its symmetric modified version will be introduced, and the sketch of a hybrid divide-and-conquer method this special class of polynomial systems will be formulated. Then, a framework of a general purposed hybrid divide-and-conquer method for solving deficient polynomial systems will be given. Some numerical results will also be given to show the efficiency of the proposed algorithm.

#### Hamid Meziani: On the global solvability of planar vector fields, Parts 1 and 2

Feb. 3, 3:30pm - 4:30pm, DM 409A

We will discuss the solvability of first order order linear planar elliptic equations with degeneracies. Normalizations near the closed orbits will be obtained and applications to boundary value problems will be given.

• 2010

#### Laura De Carli: Old and new results on Fourier multipliers

Nov. 22, 1:00pm - 2:30pm, DM 409A

In this talk I will give the definition of Fourier multiplier and I will provide some basic example and counterexamples. In particular I will show that the characteristic function of the sphere is not a Fourier multiplier. This is a celebrated result of C. Fefferman (1971). Then I will define the Cauchy transform on a cone and I will show some new result on the L^p boundness of this operator. I will also present a number of open problems and possible direction of research in this field.

#### James Fullwood, FSU: String Dualities and Geometry

Nov. 15, 1:00pm - 2:30pm, DM 409A

String theory has been physicists' most promising candidate thus far for a quantum theory of gravity. However, as of yet there have been no phenomenological consequences of the theory that can be tested by experiment. As such, many physicists view the theory more as "fancy mathematics" than a physical theory of reality. But unlike any other theory of physics which precedes it, dualities in string theory make highly non-trivial mathematical predictions motivated by the physical arguments of the theory, which strikingly enough turn out to be true in most cases. The motto seems to be that string dualities lead to unexpected links between different categories of geometry, which mathematicians may never have realized in isolation. So from a mathematical viewpoint, string theory is quite compelling to say the least. Regardless of whether or not string theory is indeed a physical theory of reality, thinking about the world in this way has greatly broadened the horizons of 21st century mathematics. So even if the theory is false, it has not been in vain. In this talk we will briefly explore the surface of the deep waters that are string dualities and their links with geometry from a non-technical standpoint.

#### Prof. Dev Roy: Paradoxes, randomness, and short descriptions

Nov. 8, 1:00pm, DM 409C

In Logic and the theory of computing, some paradoxes have been coded to yield deep results about unsolvable problems and a strong hierarchy of information content. The talk will describe some of these results.

#### Prof. Miroslav Yotov (Part 2): Homological Mirror Symmetry and Toric Varieties

Nov. 1, 1:00pm, DM 409A

#### J. N. Singh,  Barry University: Karmarkar's Algorithm in Linear Programming and its Contributions to Computational Optimization

Oct. 26, 3:00pm, DM 409B

In this talk we present various results related to the convergence of iterates, termination of the algorithm and the choice of the step-length parameter of Karmarkar’s polynomial-time algorithm in linear programming and indicate some of its recent contributions to computational optimization and computational complexity.

#### Prof. Miroslav Yotov: Homological Mirror Symmetry and Toric VarietiesOct. 18, 1:00pm - 2:30pm, DM 409A

In the talk, we give an overview of the mathematical phenomenon known as Homological Mirror Symmetry, emphasize on the ways one constructs mirror symmetric objects, and explain the role of varieties in those constructions.

#### Prof. Gueo Grantcharov: Quaternions, split quaternions and some geometry (applications)

Oct. 4, 1:00pm - 2:30pm, DM 406A

#### Prof. Steve Hudson: Geometry of level curves of harmonic functions

Sept. 20, 1:00pm - Sept. 27, 5:00pm, DM 409A

Part I: A survey of geometric results about the zero set of a function u. We consider arc length, curvature and the area enclosed by these sets. We consider several cases, that u is harmonic, an eigenfunction of the Laplacian, or a solution of Schrodinger's equation. [Sept 20]

#### Prof. Julian Edward, FIU: An application of boundary control method to an inverse problem

Sept. 13, 1:00pm - 2:30pm, DM 409A

Suppose a circular membrane in R^2 has an unknown density which is radially dependent. Using the boundary control method, we show that this density can be recovered from certain boundary measurements.

#### Prof. Pablo Olivares, Ryerson University: Modeling Large Credit Risk Portfolios and Stochastic Correlation

Aug. 30, 1:00pm - 2:30pm, DM 409A

In the first part we study how to compute standard risk measures for credit portfolios with a large number of heterogeneous companies using Large Deviation approximation techniques. We consider random recoveries depending on the state of the economy and its impact in potential losses.

In the second part we propose some models for the pricing of multivariate derivatives under stochastic correlation and volatility. We provide approximate closed-form formulas for their prices, avoiding costly Monte Carlo simulation techniques.

#### Wei Wang: An introduction to the discontinuous Galerkin method

Aug. 25, 1:00pm - 2:30pm, DM 409C

In this talk, I will first give you a background introduction of discontinuous Galerkin (DG) method. Then I will focus on how to apply DG method to a simple 1D hyperbolic equation and give you the analysis on stability and error estimate.

• 2009

#### Math Colloquia

Dec. 10, 3:30pm - 5:00pm, CP & DM

Information about the 2009 and 2010 Math Colloquia