Feb 20
Graduate Mentoring Seminar- Prof Dane Taylor, University at Buffalo
Title: Mathematics of multilayer networks for data science and complex systems
Networks are a natural representation for datasets arising in biology (neuroscience, microbiomes and genetics), social systems (reality mining, politics and online social networks) and critical infrastructures (internet, power grid, and transportation system). Due in part to the diversity of applications, there remains a significant gap between the popular heuristics that are widely used for these systems and the development of rigorous techniques grounded on first principles in mathematics and statistics. I will describe my analyses of multilayer networks in which different layers encode different types of edges, such as complementary datatypes or a network at different instances in time. This research involves a variety of techniques (e.g., linear algebra, perturbation theory, random matrix theory, and computational topology/geometry) and is both applied and theoretical. For example, I will discuss the ranking of U.S. Mathematics Departments using data from the Mathematics Genealogy Project as well as describe the information-theoretic limitations on the detectability of communities in networks. I will focus on situations in which applied mathematics can have significant impact in network science as well as describe situations where the applications are demanding new mathematical methods.
5:00PM, Tue Feb 20 2018, 250 Math
Title: Mathematics of multilayer networks for data science and complex systems
Networks are a natural representation for datasets arising in biology (neuroscience, microbiomes and genetics), social systems (reality mining, politics and online social networks) and critical infrastructures (internet, power grid, and transportation system). Due in part to the diversity of applications, there remains a significant gap between the popular heuristics that are widely used for these systems and the development of rigorous techniques grounded on first principles in mathematics and statistics. I will describe my analyses of multilayer networks in which different layers encode different types of edges, such as complementary datatypes or a network at different instances in time. This research involves a variety of techniques (e.g., linear algebra, perturbation theory, random matrix theory, and computational topology/geometry) and is both applied and theoretical. For example, I will discuss the ranking of U.S. Mathematics Departments using data from the Mathematics Genealogy Project as well as describe the information-theoretic limitations on the detectability of communities in networks. I will focus on situations in which applied mathematics can have significant impact in network science as well as describe situations where the applications are demanding new mathematical methods.
Feb 23
G&T seminar
David Cohen (University of Chicago)
Strongly aperiodic subshifts of finite type on one-ended hyperbolic groups.
Abstract: We discuss the ways in which the geometry of a group G constrains the possible behavior of symbolic dynamical systems over G. In particular, we explain our results with Chaim Goodman-Strauss and Yoav Rieck on SFTs over hyperbolic groups.
4:00PM, Fri Feb 23 2018
We discuss the ways in which the geometry of a group G constrains the possible behavior of symbolic dynamical systems over G. In particular, we explain our results with Chaim Goodman-Strauss and Yoav Rieck on SFTs over hyperbolic groups.
Feb 26
Algebra Seminar- Xingting Wang, Temple University
Noncommutative algebra from a geometric point of view
4:00PM, Mon Feb 26 2018, 250 Math Bldg.
In this talk, I will discuss how to use algebro-geometric and Poisson
geometric methods to study the representation theory of 3-dimensional
Sklyanin algebras, which are noncommutative analogues of polynomial
algebras of three variables. The fundamental tools we are employing in
this work include the noncommutative projective algebraic geometry
developed by Artin-Schelter-Tate-Van den Bergh in 1990s and the theory
of Poisson order axiomatized by Brown and Gordon in 2002, which is
based on De Concini-Kac-Priocesi’s earlier work on the applications of
Poisson geometry in the representation theory of quantum groups at
roots of unity. This talk demonstrates a strong connection between
noncommutative algebra and geometry when the underlining algebra
satisfies a polynomial identity or roughly speaking is almost
commutative.
Mar 5
Algebra Seminar
Liang Ze Wong, University of Washington
4:00PM, Mon Mar 5 2018, 250 Math Building
The Grothendieck construction shows that the category of Grothendieck
fibrations over a base category B is equivalent to the category of
contravariant pseudofunctors from B to Cat. In this talk, I will
introduce Grothendieck fibrations for enriched categories, along with
enriched versions of the Grothendieck construction and its inverse. I
will mention some requirements on the enriching category for these
constructions to work, then consider how comodules and coactions come
into play when these requirements are not satisfied.
Mar 13
Applied Math Seminar- Guo Deng, UB
3:45PM, Tue Mar 13 2018, Math 250
Mar 19
Spring Recess
Monday, March 19, 2018