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Department of Mathematics
The City College of New York
160 Convent Avenue
New York, NY 10031

Phone: (212) 650-5346
Fax: (212) 650-6294
math@ccny.cuny.edu

Mathematics Colloquium

All talks

  • Thursday, October 24, 2019, 12:30PM, NAC 6/113

    Sebastian Franco (CCNY), Graded Quivers, Generalized Dimer Models and Toric Geometry

    The open string sector of the topological B-model model on CY (m+2)-folds is described by m-graded quivers with superpotentials. This connection extends to general m the celebrated correspondence between CY (m+2)-folds and quantum field theories in (6-2m) 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 m-dimers, which fully encode the m-graded quivers and their superpotentials in the case of toric CY (m+2)-folds. Generalizing the standard m=1 case, m-dimers significantly simplify the map between geometry and m-graded quivers.

  • Thursday, October 10, 2019, 12:30PM, NAC 6/113

    Edmund Karasiewicz (Ben Gurion University), A Local Shimura Correspondence in the Wild Case

    Half-integral 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 half-integral 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 Bou-Rabee (U. Chicago), Scaling limit of the random Abelian Sandpile

    The Abelian sandpile is a simple combinatorial model from statistical physics which produces striking fractal-like 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 Tiling

    We 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 dynamics

    Motivated 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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