Our colloquia feature researchers from around the world sharing their accomplishments and insights.

## 2019 Colloquia

#### 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

#### 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

#### How stochastic shocks influence a determistic 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

#### 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

#### 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.

#### TBA

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

#### Francisco Cala-Rodriguez

**Speaker:** Francisco Cala-Rodriguez, Universidad Austral de Chile**Date:** March 28**Time:** 3:45pm-4:45pm**Room:** DM 409A

#### Alexander Stokolos

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

## Past Years

- 2018
#### Speaker: Ryan Integlia, Review of efforts towards bioinspired design and strategy to integrated networked wearables, gaming

and robotic systemsNov. 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

Speaker: Deborah L. Goldwasser \ Please click the heading for more information.

#### 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 ProcessingFeb. 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 totheoretical 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 inH . #### 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 dimensionsMar. 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 UniversityFeb. 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. Infirst 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 analyticpde . The talk will be accessible to undergraduate and graduate students majoring in math, physicsand engineering.#### Solvability near the characteristic set for a class of

first order linear partial differential operatorsMar. 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 / Wepresent 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 fordiscretized heat equationNov. 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 averaged rate of heat transport in the vertical direction, quantified as the Nusselt number, within the Rayleigh-Benard model for convection.long time**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 $(M,\omega)$ withan $ \omega$- compatible Einstein metric is Kaehler. This isa 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 tothree 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 ApplicationsNov. 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 thathave 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 differentmaterials, and certain elliptic systems associated with climate problems, which describe the evolution of atmospheric sea-level temperatures for relatively longtime 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 AHC3110 . This will be heldThursday 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 ProblemAug. 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 affinejump 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 thiswork 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. Inparticular 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 compellingto 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 of21st century mathematics. So even if the theory is false, it has not been in vain. In thistalk 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 Varieties

Oct. 18, 1:00pm - 2:30pm, DM 409AIn 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 problemSept. 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 impactin 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