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# Departmental Colloquia

Our department is proud to host weekly colloquium talks featuring research by leading mathematicians from around the world. Most colloquia are held on Fridays at 4pm in Parker Hall, Room 250 (unless otherwise advertised) with refreshments preceding at 3:30pm in Parker Hall, Room 244.

**DMS Colloquium: Kui Ren**

**Jan 17, 2020 04:00 PM**

Speaker: **Kui Ren**, Columbia University

Title: Inverse data matching with the quadratic Wasserstein distance

Abstract: Inverse data matching problems aim at finding inputs of mathematical models such that the outputs of the models match given measured data. Numerical solutions of such inverse problems have been mainly based on least-square techniques where one seeks the solutions to the problems as minimizers of an objective function that measures the mismatch between model predictions and measured data. In recent years, the quadratic Wasserstein distance has been proposed as an alternative to the classical \(L^2\) distance for measuring data mismatch in inverse matching problems. Extensive computational evidences showing the advantages of using the Wasserstein distance has been reported. The objective of this talk is to provide some mathematical explanations on the numerically-observed differences between results based on the quadratic Wasserstein distance and those based on the \(L^2\) distance for general linear and nonlinear inverse data matching problems.

This talk is based on joint works with Yunan Yang and Bjorn Engquist.

Faculty host: Junshan Lin

**DMS Colloquium: Italo Lima**

**Nov 08, 2019 04:00 PM**

Speaker: **Italo Lima**, Data Scientist at Facebook

Title: Data Science: What, Why, and How? From Academia to Industry

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Abstract: For the first part of the talk, we will review what Data Science is, why it is important, and how to connect the academia to the industry. Further, we will explain how Data Science can be used in the Infrastructure domain and provide some of the challenges in this area in the second part of the talk.

Faculty host: Nedret Billor

**DMS Colloquium: Dr. Robert Lipton**

**Oct 25, 2019 04:00 PM**

Speaker: **Prof. Robert Lipton**, LSU

Title: Manipulating light with photonic crystals

Abstract: Photonic crystals are patterned materials whose electromagnetic properties are controlled by their internal structure. Destructive interference can occur giving rise to frequency intervals where no waves can propagate inside the material (a band gap). These are the well-known photonic band gap crystals; their effects include the structural coloration of butterfly wings and have been used in ingenious ways for optical communication. In this lecture we provide a brief history of photonic band gap crystals and a window into the design of maximal band gaps using high contrast patterned dielectric media. Of particular interest is how the quasi-static resonance spectra of the structure plays a role in obtaining explicit formulas for band gaps.

Faculty host: Junshan Lin

**DMS Colloquium: Saeed Nasseh**

**Oct 18, 2019 04:00 PM**

Speaker: **Saeed Nasseh**, Georgia Southern University

Title: Modules over ﬁnite dimensional algebras with an application to a conjecture in commutative algebra

Abstract: When \(F\) is a ﬁeld and \(R\) an \(F\)-algebra, it is often important to classify the \(R\)-module structures carried by some ﬁxed \(F\)-vector space \(V\). We will describe a classical approach to that problem, which involves some algebraic geometry and homological algebra. We will then sketch new developments of these techniques and their application to the proof of a result in commutative algebra, conjectured by Vasconcelos in 1974.

Biographical sketch

Saeed Nasseh is an associate professor in the Department of Mathematical Sciences at Georgia Southern University. Prior to that, he was a postdoctoral fellow at the University of Nebraska-Lincoln. His research areas are commutative algebra and homological algebra with some overlaps with algebraic geometry, algebraic topology, and representation theory. A major part of his recent research focuses on developing and applying differential graded (DG) homological techniques to solve problems on the vanishing of homology and cohomology over commutative rings. For instance, in a joint work with Sather-Wagstaff, using the DG methods and geometric aspects of representation theory, they provided a complete solution to a long-standing conjecture posed by Vasconcelos in 1974. In other recent (in-progress) joint works with Avramov, Iyengar, and Sather-Wagstaff again using the DG techniques, they introduce several classes of commutative noetherian local rings that satisfy another major conjecture from 1975, known as the Auslander-Reiten Conjecture (which originates from representation theory of Artin algebras). He is currently working (in separate projects with other collaborators) on developing DG methods in order to completely solve this conjecture. His past and recent results on the vanishing of (co)homology, ring homomorphisms, and homological dimensions are contained in 16 research papers to date, most of which have been published in top journals.

Faculty host: Overtoun Jenda

**DMS Colloquium: Charles E. Chidume**

**Oct 04, 2019 04:00 PM**

Speaker: **Charles E. Chidume**, FTWAS, FAS, FNMS

Title: On the Strong Convergence of the Proximal Point Algorithm of Martinet and Rockafellar

Abstract: Rockafellar proved that the sequence of the celebrated proximal point algorithm introduced by Martinet for approximating a zero of a maximal monotone operator on a real Hilbert Space converges weakly. He then posed the following question: Does the sequence converge strongly? This was resolved in the negative by Guder. Consequently, several authors over the years, proposed various involved modifications of the proximal point algorithm to obtain strong convergence. In this talk, we present our new iterative algorithm, recently introduced which is totally different from the proximal point algorithm or any of its modifications, and yields strong convergence to a zero of a maximal monotone map even in real Banach spaces much more general than real Hilbert spaces. Finally, we present numerical examples to illustrate the strong convergence of the sequence of our algorithm.

Biographical sketch

Charles Ejike Chidume received his PhD degree in Mathematics from The Ohio State University, Columbus, Ohio. He returned immediately to his home country, Nigeria and worked at the University of Nigeria, Nsukka, for six years during which he rose to the rank of full professor of Mathematics. He then moved, on invitation, to join the International Centre for Theoretical Physics (ICTP) of IAEA and UNESCO of the United Nations, in Trieste, Italy, where he worked as the coordinator of the Postgraduate Diploma Program (Mathematics) and Research Mathematician. In 2009, Professor Chidume, on invitation, joined the African University of Science and Technology (AUST), a Nelson Mandela Institution offering only Postgraduate programs, located in Abuja, Nigeria. He is currently at this University serving as the Department Head of Pure and Applied Mathematics, Director of the Mathematics Institute, and Acting President of the University.

Professor Chidume has supervised 19 PhD theses and over 80 MSc and Postgraduate Diploma of the ICTP thesis. He publishes copiously and is an Associate Editor in several top journals.

Faculty host: Geraldo de Souza, Professor Emeritus

**DMS Colloquium: Virginia Vassilevska Williams**

**Sep 27, 2019 04:00 PM**

Speaker: **Virginia Vassilevska Williams** (MIT)

Title: Limitations on All Known (and Some Unknown) Approaches to Matrix Multiplication

Abstract: In this talk we will consider the known techniques for designing Matrix Multiplication algorithms. The two main approaches are the Laser method of Strassen, and the Group theoretic approach of Cohn and Umans. We define generalizations that subsume these two approaches: the Galactic and the Universal method; the latter is the most general method there is. We then design a suite of techniques for proving lower bounds on the value of \(\omega\), the exponent of matrix multiplication, which can be achieved by algorithms using many tensors \(T\) and the Galactic method. Some of our techniques exploit `local' properties of \(T\), like finding a sub-tensor of \(T\) which is so `weak' that \(T\) itself couldn't be used to achieve a good bound on $\omega$, while others exploit `global' properties, like \(T\) being a monomial degeneration of the structural tensor of a group algebra.

The main result is that there is a universal constant \(\ell>2\) such that a large class of tensors generalizing the Coppersmith-Winograd tensor \(CW_q\) cannot be used within the Galactic method to show a bound on \(\omega\) better than \(\ell\), for any \(q\). We give evidence that previous lower-bounding techniques were not strong enough to show this.

The talk is based on joint work with Josh Alman, which appeared in FOCS 2018. More recently, Alman showed how to extend our techniques so that they apply to the Universal method as well. In particular, Alman shows that the Coppersmith-Winograd tensor cannot yield a better bound on \(\omega\) than 2.16805 even using the Universal method.

Faculty host: Luke Oeding

Last Updated: 09/11/2015