Mathematics Colloquium
All talks

Thursday, March 05, 2020, 12:30PM, NAC 6/113
Nick Costanzino (NYU), A unified theory of default modelingCredit risk models largely bifurcate into two classes — the structural models and the reduced form models. Attempts have been made to reconcile the two approaches by adjusting filtrations to restrict information ( for instance Cetin, Jarrow, Protter & Yldrm, Jarrow & Protter, and Giesecke) but they are technically complicated and tend to approach filtration modification in an adhock fashion. Here we propose a reconciliation inspired by actuarial science’s approach to survival analysis whereby we model the survival and hazard rate curves themselves as a stochastic processes. The key to the unification is extending the notion of hazard rates and survival curves to the appropriate function spaces. This puts default models in a form resembling the HeathJarrowMorton (HJM) framework for interest rates and yields a unified framework for default modeling, and in particular we can talk about the hazard rate of structural models. Joint work with Albert Cohen & Harvey Stein.

Thursday, December 05, 2019, 12:30PM, NAC 6/113
Nicholas Vlamis (Queens College), Topological ends and the classification of surfacesThe classification of compact surfaces is a foundational result in topology dating back to the late 18th and early 19thcentury. Though much less known, there is a classification of all secondcountable surfaces, which relies on the theory of ends. In this talk, I will discuss the notion of a topological end and go over the classification of all surfaces due to Kerékjártó and Richards. This talk is motivated by the recent interest in studying homeomorphisms of noncompact surfaces, where this classification is essential.

Thursday, October 31, 2019, 12:30PM, NAC 6/113
LouisPierre Arguin (Baruch College), Large Values of the Riemann Zeta Function in Short IntervalsIn a seminal paper in 2012, Fyodorov & Keating proposed a series of conjectures describing the statistics of large values of zeta in short intervals of the critical line. In particular, they relate these statistics to the ones of logcorrelated Gaussian fields. In this lecture, I will present recent results that answer many aspects of these conjectures. Connections to problems in number theory will also be discussed.

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.
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