## October 2014

### Colloquium – Dr. Chiu-Yen Kao, Claremont McKenna College

Shape Optimization Problems Involving Eigenvalues and Their Applications Since Lord Rayleigh conjectured that the disk should minimize the first Laplace-Dirichlet eigenvalue among all shapes of equal area more than a century ago, eigenvalue optimization problems have been active research topics with applications in various areas including mechanical vibration, electromagnetic cavities, photonic crystals, and population dynamics. In this talk, we will review some interesting classical problems and discuss some recent developments.

Find out more »## February 2015

### Colloquium – Ming Yan, University of California, Los Angeles

Parallel and distributed optimization Abstract: Due to the explosion in size and complexity of modern datasets, both the decentralized collection or storage of these datasets as well as accompanying parallel and distributed solution methods are either necessary or at least highly desirable. In this talk, I will introduce several ways to move from single threaded optimization algorithms to parallel and distributed approaches with examples: direct parallel and distributed implementation, reformulation of the problem, and new algorithms suitable for parallel and…

Find out more »## December 2015

### Putnam Mathematical Competition

The William Lowell Putnam Mathematical Competition is an annual math competition for undergraduate students enrolled at institutions of higher learning in the United States and Canada. The competition was founded by Elizabeth Lowell Putnam in memory of her husband William Lowell Putnam, who was an advocate of intercollegiate intellectual competition. The exam has been offered annually since 1938 and is administered by the Mathematical Association of America.

Find out more »## April 2017

## May 2017

### Applied Math Seminar – Shibin Dai

Phase-Field Free Energy and Boundary Force for Molecular Solvation Abstract: We discuss a phase-filed variational model for the solvation of charged molecules with implicit solvent. The solvation free-energy functional of all phase fields consists of the surface energy, solute excluded volume and solute-solvent van der Waals dispersion energy, and electrostatic free energy. The last part is defined through the electrostatic potential governed by the Poisson-Boltzmann equation in which the dielectric coefficient is defined through a phase field. We prove Gamma-…

Find out more »## September 2017

### Join the Association of Women in Mathematics Student Chapter

Come join us for the start of the AWM Student Chapter at the University of Alabama! Free food! CONNECT with and LEARN from female mathematicians! Free membership to AWM (plus a newsletter subscription)! Who can join? Undergraduate & Graduate Students Faculty Men & Women All Majors

Find out more »## October 2017

### Colloquium – Zhimin Zhang, Wayne State University

Topic: Polynomial Preserving Recovery for Gradient and Hessian Abstract: Post-processing techniques are important in scientific and engineering computation. One of such technique, Superconvergent Patch Recovery (SPR) proposed by Zienkiewicz-Zhu in 1992, has been widely used in finite element commercial software packages such as Abaqus, ANSYS, Diffpack, etc.; another one, Polynomial Preserving Recovery (PPR) has been adopted by COMSOL Multiphysics since 2008. In this talk, I will give a survey for the PPR method and discuss its resent development to obtain the Hessian matrix…

Find out more »## November 2017

### Colloquium – Xiaoming Huo, Georgia Institute of Technology

Title: Statistically and Numerically Efficient Independence Test The big data is a well-known phenomenon in the modern world. The emerging discipline of data science has inspired a lot of discussion and debate in the scientific research communities, including the mathematical and statistical science community. Contributing to this discussion, in the first part of this talk, I will present a discussion as well as a selective survey on the landscape of data science, as it is forming its foundation. On the…

Find out more »## January 2018

### Colloquium – John Etnyre, Georgia Institute of Technology

Topic: Curvature and contact topology Abstract: Contact geometry is a beautiful subject that has important interactions with topology in dimension three. In this talk I will give a brief introduction to contact geometry and discuss its interactions with Riemannian geometry. In particular I will discuss a contact geometry analog of the famous sphere theorem and more generally indicate how the curvature of a Riemannian metric can influence properties of a contact structure adapted to it. This is joint work with…

Find out more »## February 2018

### Algebra/Topology Seminar – Patricia Cahn (Smith College)

Title: Colored Tri-Plane Diagrams and the Slice-Ribbon Problem Abstract: We study dihedral branched covers of the four-dimensional sphere, where the branching set is a surface with one singularity modeled on the cone on a knot K. We construct examples of these covers using colored tri-plane diagrams, which are triples of tangles that can be used to describe a surface in the four-sphere. We also show that a knot invariant arises in this context, which can potentially be used to prove…

Find out more »## March 2018

## April 2018

### Colloquium – Julie Mitchell (Oak Ridge National Laboratory)

ABSTRACT flyer - Julie Mitchell

Find out more »### Colloquium – Maria Laura delle Monache (Inria Grenoble – Rhône Alpes)

Topic: Control of traffic flow: from ramp metering to autonomous vehicles Abstract: In this talk, we will consider different control frameworks for traffic flow. In particular, we will show the evolution of traffic control from classical strategies (for example ramp-metering) to more modern approaches using autonomous vehicles. We will introduce different ways to describe mathematically the phenomenon by using scalar conservation laws and coupled PDE-ODE models, modeling traffic dynamics with a macroscopic approach and presenting different control techniques that could…

Find out more »## August 2018

### Applied Math Seminar, Oleksii Beznosov, University of Colorado Boulder

Seminar Title: High order hybrid Hermite-discontinuous Galerkin overset grid methods for the wave equation

Find out more »### Applied Math Seminar – Chuntian Wang, University of Alabama

Title: Initial and boundary value problems for the deterministic and stochastic Zakharov-Kuznetsov equation in a bounded domain

Find out more »## September 2018

### Applied Math Seminar – Dang Nguyen, University of Alabama

Title: A Multi-scale Approach to Limit Cycles with Random Perturbations Involving Fast Switching and Small Diffusion Abstract: This talk is devoted to multi-scale stochastic systems. The motivation is to treat limit cycles under random perturbations involving fast random switching and small diffusion, which are represented by the use of two small parameters. Associated with the underlying systems, there are averaged or limit systems. Suppose that for each pair of the parameters, the solution of the corresponding equation has an invariant…

Find out more »### Colloquium, William T. Trotter, Georgia Institute of Technology

Title: The Top Ten Theorems in the Combinatorics of Posets

Find out more »### Applied Math Seminar – Yichuan Zhao, Georgia State University

Title: Empirical likelihood for the bivariate survival function under univariate censoring Abstract: The bivariate survival function plays an important role in multivariate survival analysis. Using the idea of influence functions, we develop empirical likelihood confidence intervals for the bivariate survival function in the presence of univariate censoring. It is shown that the empirical log-likelihood ratio has an asymptotic standard chi-squared distribution with one degree of freedom. A comprehensive simulation study shows that the proposed method outperforms both the traditional normal…

Find out more »### AWM Seminar – Elizabeth Peplinski, Alabama Insurance Society

The University of Alabama Chapter of the Association for Women in Mathematics is inviting you to attend Elizabeth Peplinski's talk on Actuary Science. Elizabeth Peplinski is the Acturial Chair of the Alabama Insurance Society, a student organization for people interested in careers in the insurance industry. This will be a unique opportunity to learn about this great career field and get some insights on the recruitment process. This talk will take place on Monday, September 17, 2018 , from 3:00…

Find out more »### Applied Math Seminar – Haomin Zhou, Georgia Institute of Technology

Title: Optimal Transport on Finite Graphs with Applications Abstract: In this talk, I will discuss the optimal transport theory on discrete spaces. Various recent developments related to free energy, Fokker-Planck equations, as well as Wasserstein distance on graphs will be presented, some of them are rather surprising. Applications in game theory and robotics will be demonstrated. This presentation is based on several joint papers with Shui-Nee Chow (Georgia Tech), Wen Huang (USTC), Wuchen Li (UCLA), Yao Li (U. Mass), Jun…

Find out more »## October 2018

### Colloquium – Rodrigo Bañuelos, Purdue University

Title: On the discrete Hilbert transform Abstract: The discrete Hilbert transform, acting on the space of (doubly infinite) sequences, was introduced by David Hilbert at the beginning of the 20th century. It is the discrete analogue of the continuous Hilbert transform acting on functions on the real line (conjugate function in the periodic case). In 1925, M. Riesz proved the Lp boundedness, for p larger than one and finite, of the continuous version, thereby solving a problem of considerable…

Find out more »## January 2019

### Applied Math Seminar – Shibin Dai, University of Alabama

Title: Mean field models for thin film droplet coarsening Abstract: A thin liquid film coating a solid substrate is unstable and the late stage morphology is essentially quasiequilibrium droplets connected by an ultra thin film. Droplets exchange mass and coarsening occurs — the total number of droplets N(t) decreases while the average size of droplets increases. It is predicted that N(t) obeys a power law $N(t) \sim ct^{-2/5}$ in the 1D case. For the physically realistic case when the underlying…

Find out more »### Applied Math Seminar – Brendan Ames, University of Alabama

Title: Exact clustering by semidefinite programming under the heterogeneous planted cluster model. Abstract: Clustering, or the sorting of data into groups of similar items, is a fundamental task in machine learning and statistical analysis. Until recently, most computational methods for clustering relied on heuristics with no theoretical guarantee ensuring that clusters present in the data would be correctly identified. In this talk, I will present recent results partially addressing this issue. Specifically, I will discuss a new probabilistic model for…

Find out more »## February 2019

### Applied Math Seminar – Yuhui Chen, University of Alabama

Title: Bayesian Nonparametric Models and Its Applications Abstract: Polya tree priors are random probability measures that are easily centered at standard parametric families, such as the normal. As such, they provide a convenient avenue toward creating a parametric/nonparametric model for data. Briefly, we center a Polya tree at an initial parametric guess on data; then by adding more details via data, departures from the initial guess will be captured and used for adjusting the guess to obtain a robust nonparametric…

Find out more »### Analysis Seminar – Christoph Fischbacher, University of Alabama at Birmingham

Title: Area Laws for the Entanglement in the XXZ spin chain Abstract: The question on how to rigorously define and prove Many-Body-Localization (MBL) phenomena has attracted significant interest over the recent years. In this talk, we will give a physical motivation for the so-called entanglement entropy (EE) and explain why an area law for the EE can be interpreted as a sign of MBL. We then introduce the Heisenberg XXZ spin Hamiltonian, which is unitarily equivalent to a direct sum of discrete many-particle Schrödinger operators…

Find out more »### Applied Math Seminar – Shibin Dai, University of Alabama

Title: Degenerate Diffusion in Phase Separations Abstract: Phase separations are widely observed phenomena in materials science. One model of phase separation is the Cahn-Hilliard equation with a smooth double-well potential, and with phase-dependent diffusion mobilities. The latter is a feature of many materials systems and makes the analysis and accurate numerical simulations challenging. In this talk I will discuss three aspects of the degenerate Cahn-Hilliard equations: 1. the sharp-interface limit via asymptotic analysis, and the dynamics in different time scales;…

Find out more »### Research Talk – Xin Zhou, University of California, Santa Barbara

Title: Multiplicity One Conjecture in Min-max theory Abstract: I will present a recent proof of the Multiplicity One Conjecture in Min-max theory. This conjecture was raised by Marques and Neves as the key step to establish a Morse theory for the area functional. It says that in a closed manifold of dimension between 3 and 7 with a bumpy metric, the min-max minimal hypersurfaces associated with the volume spectrum introduced by Gromov, Guth, Marques-Neves are all two-sided and have multiplicity one. As…

Find out more »### Analysis Seminar – Joe Renzi, University of Alabama

Title: Two-sided Mullins-Sekerka flow does not preserve convexity, after Uwe F. Mayer Abstract: The (two-sided) Mullins-Sekerka model is a nonlocal evolution model for closed hypersurfaces, which was originally proposed as a model for phase transitions of materials of negligible specific heat. Under this evolution the propagating interfaces maintain the enclosed volume while the area of the interfaces decreases. We will show by means of an example that the Mullins-Sekerka flow does not preserve convexity in two space dimensions, where we consider…

Find out more »## March 2019

### Colloquium – Ken Ono, Emory University

Topic: Polya’s Program for the Riemann Hypothesis and Related Problems Abstract: In 1927 Polya proved that the Riemann Hypothesis is equivalent to the hyperbolicity of Jensen polynomials for Riemann’s Xi-function. This hyperbolicity has only been proved for degrees d=1, 2, 3. We prove the hyperbolicity of 100% of the Jensen polynomials of every degree. We obtain a general theorem which models such polynomials by Hermite polynomials. This theorem also allows us to prove a conjecture of Chen, Jia, and Wang…

Find out more »### Colloquium – Karen Parshall, Commonwealth Professor of Mathematics and History, University of Virginia

Title: The Roaring Twenties in American Mathematics Abstract: World War I served as a break in business as usual within the American mathematical research community. In its aftermath, American mathematicians had the sense, in Oswald Veblen’s words, of entering into “a new era in the development of our science.” To that end, “very nerve,” according to Roland Richardson, “should be strained to get our research back on its feet.” These and others poured themselves into their work in the 1920s,…

Find out more »### Applied Math Seminar – Steven Wise, University of Tennessee

Title: Convergence Analyses of some Nonlinear Multi-Level Algorithms for Non-Quadratic Convex Optimization Problems via Space Decomposition and Subspace Correction Abstract: Nonlinear multi-level methods, such as the full approximation storage (FAS) multigrid scheme, are widely used solvers for nonlinear problems. In this presentation, a new framework to analyze FAS-type methods for convex optimization problems is developed. FAS can be recast as an inexact version of a nonlinear multigrid method based on space decomposition and subspace correction, namely the successive subspace optimization…

Find out more »## April 2019

### Analysis Seminar – Ryan Berndt, Otterbein University

Title: Two-weight problem for the Fourier transform. Abstract: We examine the problem of the Fourier transform mapping one weighted Lebesgue space into another, by studying necessary conditions and sufficient conditions which expose an underlying geometry. In the necessary conditions, this geometry is connected to an old result of Mahler concerning the the measure of a convex body and its geometric polar being essentially reciprocal. An additional assumption, that the weights must belong to a reverse Hölder class, is used to…

Find out more »### Colloquium – Mark Behrens, University of Notre Dame

Title: "Current themes in the study of the homotopy groups of spheres" Abstract: I will summarize the current state of affairs of the study of the stable homotopy groups of spheres, and will describe some connections to algebraic and differential geometry.

Find out more »### Applied Math Seminar – Rongjie Lai, Rensselaer Polytechnic Institute

Title: Understanding Manifold-structured Data via Geometric Modeling and Learning Abstract: Analyzing and inferring the underlying global intrinsic structures of data from its local information are critical in many fields. In practice, coherent structures of data allow us to model data as low dimensional manifolds, represented as point clouds, in a possible high dimensional space. Different from image and signal processing which handle functions on flat domains with well-developed tools for processing and learning, manifold-structured data sets are far more challenging…

Find out more »### Applied Math Seminar – Trang Dinh, University of Alabama

Title: Understanding Tensor and Tensor Decompositions Abstract: Tensors are multidimensional arrays that can play a key role in the representation of big data. Decompositions of higher-order tensors have applications in biochemistry, signal processing, data mining, neuroscience, and elsewhere. The talk will present commonly used tensor operations and different types of tensor decomposition. Specifically, it will illustrate the CANDECOMP/PARAFAC (CP) decomposition and the Tucker decomposition, which are examples of decompositions that have been employed to optimize the storage of large high-order…

Find out more »### Colloquium – Xiaofan Li, Illinois Institute of Technology

Title: Numerical simulations of macroscopic quantities for stochastic differential equations with alpha-stable processes Abstract: The mean first exit time, escape probability and transitional probability density are utilized to quantify dynamical behaviors of stochastic differential equations with non-Gaussian, $\alpha$-stable type L\'evy motions. Taking advantage of the Toeplitz matrix structure of the time-space discretization, a fast and accurate numerical algorithm is proposed to simulate the nonlocal Fokker-Planck equations on either a bounded or infinite domain. Under a specified condition, the scheme is…

Find out more »### Applied Math Seminar – Dengfeng Sun, Purdue University

Title: Improving the Convergence Rate of the Distributed Gradient Descent Method Abstract: This talk presents our recent work on the accelerated Distributed Gradient Descent (DGD) method for distributed optimization problems. We observed that the inexact convergence of the DGD algorithm can be caused by the inaccuracy in the consensus procedure in a distributed optimization setting. Motivated by this observation, we try to develop a sufficiently accurate consensus method in order for a better convergence result. In our work, it is…

Find out more »### Analysis Seminar – Khalid Said, University of Alabama

Abstract In this presentation we examine some useful properties of the numerical range. We explore two dierent positions , generic and generalized generic positions. We show that two pairs of subspaces (M,N) and (M?;N?) are unitarily equivalent if M and N are subspaces of Cn in generic position by constructing a unitary operator. We establish the relationships between two sets of the principal angles, the principal angles between M and N and the principal angles between M? and N?. We…

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