Division of Science





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

Phone: (212) 650-5346
Fax: (212) 650-6294

Mathematics Colloquium

All talks

  • Thursday, March 05, 2020, 12:30PM, NAC 6/113

    Nick Costanzino (NYU), A unified theory of default modeling

    Credit 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 ad-hock 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 Heath-Jarrow-Morton (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 surfaces

    The classification of compact surfaces is a foundational result in topology dating back to the late 18th- and early 19th-century. Though much less known, there is a classification of all second-countable 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 non-compact surfaces, where this classification is essential.

  • Thursday, October 31, 2019, 12:30PM, NAC 6/113

    Louis-Pierre Arguin (Baruch College), Large Values of the Riemann Zeta Function in Short Intervals

    In 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 log-correlated 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 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.

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