Mathematics Colloquium Winter 2017

Tuesdays - 4:00 p.m.
McHenry Library Room 4130
Refreshments served at 3:30 in the Tea Room (4161)
For further information please contact Professor Junecue Suh or call the Mathematics Department at 459-2969


Tuesday, January 10, 2017

NO COLLOQUIUM


Tuesday, January 17,2017

Chenyang Xu, Beijing International Center of Mathematics Research

Title: Dual Complex of a Singular Pair

Abstract: The topology of an algebraic variety is a central subject in algebraic geometry. Instead of a variety, we consider the topology of a pair (X,D) which is a variety X with a divisor D, but in the coarsest level. More precisely, we study the dual complex defined as the combinatorial datum characterizing how the components of D intersect with each other. We will discuss how to use the minimal model program (MMP) to investigate it. As one concrete application, we will explain how close the dual complex of a log Calabi-Yau pair (X,D) is to a finite quotient of a sphere.


Tuesday, January 24, 2017

Jenny Wilson, Stanford University

Title: Stability in the homology of configuration spaces

Abstract: 
This talk will illustrate some topological properties of the space Fk(M) of ordered k-tuples of distinct points in a manifold M. For a fixed manifold M, as k increases, we might expect the topology of the configuration spaces Fk(M) to become increasingly complicated. Church and others showed, however, that when M is a connected and open, there is a representation-theoretic sense in which these configuration spaces stabilize.  In this talk I will explain these stability patterns, and how they generalize classical notions of homological stability proved by McDuff and Segal in the 1970s. I will describe higher-order "secondary stability" phenomena established in recent work joint with Jeremy Miller.  
 

Tuesday, January 31, 2017


Tuesday, February 7, 2017


Thursday, February 9, 2017


Tuesday, February 14, 2017


Thursday, February 16, 2017

Oleksandr Tsymbaliuk, Stony Brook University

Title: Shifted Yangians and Shifted Quantum Affine Algebras

Abstract: 

In this talk, I will speak about the shifted versions of Yangians and quantum affine algebras as well as their incarnations through geometry of parabolic Laumon spaces, additive/multiplicative slices, and Todda lattice.
I will start by reminding the notion of the shifted Yangian (originally introduced by Brundan-Kleshchev in the gl(n) case with a dominant shift and later generalized by Kamnitzer-Webster-Weekes-Yacobi to any simple Lie algebra with an arbitrary shift) as well as the recent work relating these algebras to the Coulomb branches.
In the second half, I will discuss the multiplicative analogue of that story (which is a joint project with Michael Finkelberg). On the algebraic side this leads to the notion of shifted quantum affine algebras, while on the geometric side we replace cohomology by K-theory and additive slices are replaced by multiplicative slices.

Tuesday, February 21, 2017

Ricardo Sanfelice, University of California, Santa Cruz

Title: Structural Properties and Tools for Robustness in Hybrid Systems: Flows, Jumps, Zeno, and other Misbehaviors

Abstract:  Hybrid systems have become prevalent when describing control systems that mix continuous and impulsive dynamics. Continuous dynamics usually govern the evolution of the physical variables in a system, while impulsive (or discrete) behavior is typically due to events in the control algorithm or abrupt changes in the dynamics. A mathematical framework comprised of differential and difference equations/inclusions with constraints will be introduced to model, analyze, and design such systems. An appropriate notion of solution and basic properties on the system data guaranteeing sequential compactness of solutions will be introduced. Tools for the analysis and synthesis of robust hybrid feedback control systems will be presented. The focus will be on asymptotic stability, invariance of sets, and robustness. The tools will be exercised in examples throughout the talk. Relevant applications in science and engineering will be highlighted. 


Tuesday, February 28, 2017

Andras Vasy, Stanford University


Tuesday, March 7, 2017

Tomoyuki Arakawa, Research Institute for Mathematical Sciences Kyoto University


Thursday, March 16, 2017

*SPECIAL Mathematics Colloquium*

Yitang Zhang, University of California, Santa Barbara


Tuesday, March 21, 2017

NO COLLOQUIUM