Calendar

Tomorrow

Student Commutative Algebra Seminar, Mr. Daniel Shankman, Purdue University, REC 113

Monday, Jan 22 3:30 pm - 4:30 pm

Groupes Reductifs sur un Corps Local II

Bridge to Research, Prof. Steve Bell, Purdue University, UNIV 003

Monday, Jan 22 4:30 pm - 5:30 pm

A surefire way to find new results about old things

I will tell the story of how my PhD thesis advisor, Norberto Kerzman, and his mentor, Eli Stein, discovered a new property of the centuries old Cauchy integral and how it has influenced the way I think about complex analysis. I have tried to use the Kerzman-Stein modus operandi in my own research, and once in a while, it has led me to find shiny new things in moldy corners of the basement of complex analysis.

Next Week

Commutative Algebra Seminar, Prof. Giulio Caviglia, Purdue University, UNIV 101

Wednesday, Jan 24 1:30 pm - 2:20 pm

Some Cases of the Lex-Plus-Powers Conjecture.

Spectral and Scattering Theory Seminar, Melinda Lanius, UIUC, MATH 431

Wednesday, Jan 24 1:30 pm - 2:30 pm

Scattering symplectic geometry

Abstract: Scattering-symplectic manifolds are manifolds equipped with a type of minimally degenerate Poisson structure that is not too restrictive so as to have a large class of examples, yet restrictive enough for standard Poisson invariants to be computable. We will define scattering-symplectic geometry, providing plenty of examples, and discuss connections with contact geometry.

Probability Seminar, Prof. Aaron Yip, Purdue University, REC 113

Wednesday, Jan 24 1:30 pm - 2:45 pm

Long Time Behavior of Brownian Motion in Tilted Periodic Potentials

We will investigate various limits concerning the long time average velocity V of a Brownian particle diffusing on a periodic potential. The prototype model is Langevin dynamics which incorporates inertia (mass) and friction. The key feature of the current work is the consideration of an additional macroscopic tilt, F. The goal is to understand how the average velocity V depends on F. Interesting thresholds for the value of F can be obtained, in particular under the limit of vanishing friction and noise. Using the averaging theory of Freidlin-Wentzel, the current work provides rigorous mathematical justification of some formulas obtained by Risken. An earlier, fundamental result by Tanaka for Brownian particle diffusing on a random (Brownian) potential will also be discussed. This is a joint work with Liang Cheng.

Algebraic Geometry Seminar, Uli Walther, Purdue University, MATH 731

Wednesday, Jan 24 3:30 pm - 4:30 pm

GKZ-systems and mixed Hodge modules

I will define GKZ-systems, and talk a little about their properties from the algebraic, analytic, and combinatorial point of view. Then I will discuss a theorem of Gelfand et al, and a sharpening by Mathias Schulze and myself, on the question which GKZ-systems arise as (D-module-)direct image of a natural D-module on a torus. In such cases, the GKZ-system inherits a mixed Hodge module structure. I will then explain work with Thomas Reichelt that computes this MHM structure on a class of GKZ-systems that comes up naturally in mirror symmetry. Very few of such explicitly computed structures seem to be known.

Student Colloquium, Sarah Percival, Purdue University, UNIV 117

Wednesday, Jan 24 4:30 pm - 5:30 pm

An Introduction to Topological Data Analysis with a Focus on Persistent Homology

Abstract: Topological data analysis applies techniques from topology to the study of large data sets. One of the most useful tools of TDA is persistent homology, which provides a method of determining the global structure of a discrete data set. From searching for cancer biomarkers to studying swarming behavior of animals, persistent homology has been used by researchers to study a wide variety of problems outside mathematics.

CCAM Lunch Seminar, Dr. Ashish Kumar Pandey, UIUC, REC 303

Friday, Jan 26 11:30 am - 12:30 pm

Instabilities in shallow water wave models

Abstract: Slow modulations in wave characteristics of a nonlinear, periodic traveling wave in a dispersive medium may develop non-trivial structures which evolve as it propagates. This phenomenon is called modulational instability. In the context of water waves, this phenomenon was observed by Benjamin and Feir and, independently, by Whitham in Stokes' waves. I will discuss a general mechanism to study modulational instability of periodic traveling waves which can be applied to several classes of nonlinear dispersive equations including KdV, BBM and regularized Boussinesq type equations.

Special Colloquium, Prof. Harm Derksen, University of Michigan, LWSN B155

Friday, Jan 26 3:30 pm - 4:30 pm

Constructive Invariant Theory and Noncommutative Rank

If G is a group acting on a vector space V by linear transformations, then the invariant polynomial functions on V form a ring. In this talk we will discuss upper bounds for the degrees of generators of this invariant ring. An example of particular interest is the action of the group SL_n x SL_n on the space of m-tuples of n x n matrices by simultaneous left-right multiplication. In this case, Visu Makam and the speaker recently proved that invariants of degree at most mn^4 generate the invariant ring. We will explore an interesting connection between this result and the notion of noncommutative rank.

Research Areas: Commutative rings and algebras

Two Weeks

Graduate Student Invited Colloquium Speaker, Prof. Chelsea Walton, University of Illinois at Urbana Champaign, MATH 175

Tuesday, Jan 30 3:30 pm - 4:20 pm

TBD

Algebraic Geometry Seminar, Uli Walther, Purdue University, MATH 731

Wednesday, Jan 31 3:30 pm - 4:30 pm

GKZ-systems and mixed Hodge modules

This will be a continuation of the last talk.

Automorphic Forms and Representation Theory Seminar, Prof. Jayce Getz, Duke University, UNIV 317

Thursday, Feb 1 1:30 pm - 2:20 pm

TBD

February

Department Colloquium, Prof. Guillaume Bal, University of Chicago, MATH 175

Tuesday, Feb 20 3:30 pm - 4:20 pm

TBD

Automorphic Forms and Representation Theory Seminar, Prof. Manish Patnaik, University of Alberta, UNIV 317

Thursday, Feb 22 1:30 pm - 2:20 pm

TBD

March

Math is Key Lecture, Dr. Eugenia Cheng, School of the Art Institute of Chicago

Tuesday, Mar 6 3:30 pm - 4:20 pm

TBD

Department Colloquium, Prof. Wilfrid Gangbo, UCLA, MATH 175

Tuesday, Mar 20 3:30 pm - 4:20 pm

TBD

Department Colloquium, Prof. Cristina Villalobos, University of Texas, Rio Grande Valley, MATH 175

Tuesday, Mar 27 3:30 pm - 4:20 pm

TBD

April

Department Colloquium, Prof. Dinakar Ramakrishnan, California Institute of Technology, MATH 175

Tuesday, Apr 3 3:30 pm - 4:20 pm

TBD

Department Colloquium, Prof. Frank Thorne, University of South Carolina, MATH 175

Tuesday, Apr 10 3:30 pm - 4:20 pm

TBD

Department Colloquium, Prof. Matt Gursky, University of Notre Dame, MATH 175

Tuesday, Apr 17 3:30 pm - 4:20 pm

TBD

Automorphic Forms and Representation Theory Seminar, Dr. Cris Negron, MIT, UNIV 317

Thursday, Apr 19 1:30 pm - 2:20 pm

TBD

Department Colloquium, Prof. Helene Esnault, Freie Universitat Berlin, MATH 175

Tuesday, Apr 24 3:30 pm - 4:20 pm

TBD

Automorphic Forms and Representation Theory Seminar, Prof. Helene Esnault, Freie Universitat Berlin, UNIV 317

Thursday, Apr 26 1:30 pm - 2:20 pm

TBD