Mathematics Colloquium
All talks

Thursday, October 24, 2019, 12:30PM, NAC 6/113
Sebastian Franco (CCNY), Graded Quivers, Generalized Dimer Models and Toric GeometryThe open string sector of the topological Bmodel model on CY (m+2)folds is described by mgraded quivers with superpotentials. This connection extends to general m the celebrated correspondence between CY (m+2)folds and quantum field theories in (62m) dimensions. These quivers exhibit new order(m+1) mutations, which reproduce the recently discovered dualities of the associated quantum field theories for m≤3 and generalize them to m>3. In the first part of this talk we will discuss the general framework of graded quivers, which also involves ideas on higher Ginzburg algebras and higher cluster categories.
We will then introduce mdimers, which fully encode the mgraded quivers and their superpotentials in the case of toric CY (m+2)folds. Generalizing the standard m=1 case, mdimers significantly simplify the map between geometry and mgraded quivers.

Thursday, October 10, 2019, 12:30PM, NAC 6/113
Edmund Karasiewicz (Ben Gurion University), A Local Shimura Correspondence in the Wild CaseHalfintegral weight automorphic forms provide one of the earliest examples of a connection between automorphic forms and arithmetic. Despite their utility and ubiquity, only recently Weissman extended the Langlands program to incorporate these halfintegral weight forms, the culmination of input by many mathematicians.
One important contribution that helped guide the formulation of this extension was Savin’s approach to the local Shimura correspondence. After providing some background on Shimura’s original correspondence, we will describe Savin’s approach via Hecke algebras in the tame case. Finally we will discuss some recent progress toward the local Shimura correspondence in the wild case.

Thursday, September 19, 2019, 12:30PM, NAC 6/113
Ahmed BouRabee (U. Chicago), Scaling limit of the random Abelian SandpileThe Abelian sandpile is a simple combinatorial model from statistical physics which produces striking fractallike patterns. Why do these patterns appear? What aspects of the patterns persist under the introduction of randomness?
I will introduce the model and then hint at how tools from elliptic partial differential equations and ergodic theory can be used to (partially) answer these questions.

Thursday, May 09, 2019, 12:30PM, NAC 6/114
Linda Keen (Lehman College (CUNY)), Geometry and TilingWe will show how the basic question of how to lay tiles in a room leads mathematicians to interesting questions and new concepts in geometry.

Thursday, March 28, 2019, 12:30PM, NAC 6/114
Konstantin Mischaikow (Rutgers U.), A combinatorial/algebraic topological approach to nonlinear dynamicsMotivated by the increase in data driven science I will discuss a combinatorial/algebraic topological approach to characterizing nonlinear dynamics. In particular, I will describe how order theory can be used to efficiently and effectively organize the decomposition of dynamics and how algebraic topological tools can be used to characterize the structure of the dynamics. I will then propose a definition of nonlinear dynamics based on these structures. To demonstrate the effectiveness of this approach I will consider several problems from systems and synthetic biology. I will focus on identification and rejection of network models for these types of systems based on functional form and time series data.
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