# Mathematics Colloquium Winter 2017

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:**

_{k}(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 F

_{k}(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

**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: **

**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**