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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.

**Mathematics & Statistics Colloquium: Alex Clark**

**Mar 03, 2017 04:00 PM**

Speaker: **Alex Clark**, University of Leicester (http://www2.le.ac.uk/departments/mathematics/extranet/staff-material/staff-profiles/adc20)

Title: Tiling Spaces: Their Structure and Unexpected Examples

Abstract: In this talk we will explain how one can introduce a natural topological structure to certain spaces of tilings of the plane. These spaces admit a natural dynamical system that captures many of the important properties of the tilings, including the spectral properties of associated quasicrystals. After a review of some of the fundamental results about the structure of these tiling spaces, we shall explain some recent results of Clark and Sadun that have far reaching implications for higher dimensional dynamical systems.

In particular, we shall explore a counterexample to conjectures which has the consequence that higher dimensional dynamics are fundamentally different from those of dimension one.

Faculty host: Krystyna Kuperberg

**Mathematics & Statistics Colloquium: Leslie Hogben**

**Mar 31, 2017 04:00 PM**

Speaker: **Leslie Hogben**, Iowa State University (https://math.iastate.edu/directory/leslie-hogben/)

Faculty host: T-Y Tam

**Joint Math-Bio Colloquium**

**Apr 07, 2017 04:00 PM**

Speaker: **John Rhodes** (U. Alaska, Fairbanks)

**Mathematics & Statistics Colloquium: Dr. Anuj Srivastava**

**Apr 21, 2017 04:00 PM**

Speaker: **Dr. Anuj Srivastava**, Florida State University (http://ani.stat.fsu.edu/~anuj/)

Faculty host: Guanqun Cao

**Commencement**

**Dec 16, 2017 12:00 AM**

**AU-AUM Mathematics & Statistics Colloquium: Yue Chen**

**Feb 24, 2017 04:00 PM**

Speaker: **Yue Chen**, AUM

Title: Double Negative Behavior in Metamaterials

Abstract: Metamaterials are a new form of structured materials designed to have electromagnetic properties not generally found in nature. In this talk, I will introduce a rigorous mathematical framework for controlling localized resonances and predicting exotic behavior inside optical metamaterials. The theory provides a rational basis for designing microstructure using multiphase nonmagnetic materials to create backward wave behavior across prescribed frequency ranges.

**Mathematics & Statistics Colloquium: Henry Schenck**

**Feb 17, 2017 04:00 PM**

Speaker: **Professor Henry** **Schenck,** University of Illinois** **(http://www.math.uiuc.edu/~schenck/)

Title: Hyperplane Arrangements: Algebra, Combinatorics, Topology

Abstract: A hyperplane arrangement is a collection

\[

\mathcal{A} = \bigcup\limits_{i=1}^d H_i \subseteq \mathbb{K}^n,

\]

where typically \(\mathbb{K}\) is \(\mathbb{R}\) or \(\mathbb{C}\). The complement \(X = \mathbb{K}^n \setminus \mathcal{A}\) has very interesting topology. In 1980 Orlik and Solomon determined the cohomology ring; \(H^*(X,\mathbb{Z})\) is a quotient of an exterior algebra \(E\) with a generator for each hyperplane. Surprisingly, all relations are determined by the combinatorics of \(\mathcal{A}\). Nevertheless, there remain many interesting open questions, which involve a beautiful interplay of algebra, combinatorics, geometry, and topology. I'll spend much of the talk discussing this interplay, and close by discussing several conjectures in the field, along with recent progress on those conjectures, where the Bernstein-Gelfand-Gelfand correspondence plays a key role.

Faculty host: Yanzhao Cao

**Mathematics & Statistics Colloquium: Dr. Yimin Xiao**

**Feb 14, 2017 04:00 PM**

Speaker: **Dr. Yimin Xiao**, Michigan State University

Title: Recent Developments in Theory of Random Fields

ABSTRACT: Random fields are not only important in probability, stochastic partial differential equations and statistics, but also very useful as stochastic models in many scientific areas such as biology, environmental sciences, geophysical sciences, image processing, and physics. These applications, in turn, have raised many interesting and often challenging questions for mathematicians and statisticians.For random fields indexed by the Euclidean space or spheres, their important characteristics include smoothness/roughness, self-similarity, isotropy/anisotropy, and short/long range dependence. Various mathematical and statistical methods have been developed for constructing random fields, and for studying their properties and statistical inferences.

In this talk we present some recent results on probabilistic, geometric, and analytic properties of Gaussian random fields and solutions of stochastic partial differential equations (SPDEs).

**Mathematics & Statistics Colloquium: Daniel Nakano**

**Feb 10, 2017 04:00 PM**

**Daniel Nakano**, University of Georgia

Title: Tensor Triangular Geometry and Applications

Abstract: Tensor triangular geometry as introduced by Paul Balmer is a powerful idea which can be used to extract hidden ambient geometry from a given tensor triangulated category. These geometric structures often arise at the derived/cohomological level and play an important role in understanding the combinatorial property of representations of groups and algebras.

In this talk I will first present a general setting for a compactly generated tensor triangulated category that enables one to classify thick tensor ideals and to determine the Balmer Spectrum. Several examples will be presented to illustrate these beautiful connections which includes the stable module category for finite groups and the derived category of bounded perfect complexes for finitely generated \(R\)-modules where \(R\) is a commutative Noetherian ring.

For a classical Lie superalgebra \({\mathfrak g}={\mathfrak g}_0+{\mathfrak g}_1\), I will later show how to construct a Zariski space from a detecting subalgebra \({\mathfrak f}\) and demonstrate that this topological space governs the tensor triangular geometry for the category of finite dimensional \({\mathfrak g}\)-modules that are semisimple over \({\mathfrak g}_0\). Concrete realizations will be provided for the Lie superalgebra \({\mathfrak gl}(m|n)\). This answers an old question about finding a geometric object that governs the representation theory for Lie superalgebras. If time permits, I will also discuss other new applications.

These results represent joint work with B. Boe and J. Kujawa.

**Applied Mathematics Seminar/Colloquium Yuesheng Xu**

**Feb 10, 2017 02:00 PM**

Please note time: 2:00 pm

Speaker: Professor Yuesheng Xu (Sun Yat Sen University, China)

Title: Mathematics in Data Science

Abstract: We shall discuss several mathematical problems crucial in data science. They include representation of data, mathematical models of recovering a fact from raw data, matching learning and solving optimization problems in data analysis.

Faculty host: Yanzhao Cao

**Mathematics & Statistics Colloquium: Sibylle Schroll**

**Feb 07, 2017 04:00 PM**

Speaker: **Dr. Sibylle Schroll**, University of Leicester, UK

Title: New trends in representation theory

Abstract: Cluster algebras, introduced in the early 2000s, followed by their categorifications are transforming representation theory. They have opened up the field to new techniques and methods by introducing, for example, topological geometry and surface combinatorics to the theory. In this talk, we shall see how this helped create a new framework for representation theory, leading to surprising advances towards the solution of old conjectures and to exciting new connections with modern homological algebra.

Faculty host: Ulrich Albrecht

Last Updated: 09/11/2015