See organizers Rufus, Alan or Robin for details.

Speaker: David Yuen (Lake Forest College)

Title: Modularity in Degree Two

Abstract: Modularity in degree one involves weight two elliptic modular forms. Modularity in degree two involves weight two Siegel paramodular forms.

The Paramodular Conjecture of Brumer and Kramer tells us where to look for Siegel modular forms that correspond to certain abelian surfaces defined over the rationals.

This talk focuses on computations, and we consider several ways of computing Siegel modular forms over the paramodular group in degree two. We compile, in conjunction with Brumer and Kramer’s data on abelian surfaces, substantial evidence for the Paramodular Conjecture. We discuss strong evidence for existence and nonexistence of nonlift paramodular eigenforms of weight two in general levels N up to N < 1000.

We will show how to construct a nonlift paramodular eigenform of level 277 that conjecturally corresponds to the abelian surface of conductor 277. We discuss recent work that proves that, indeed, these two objects have the same L-function, and thus the abelian surface of conductor 277 is modular.

Speaker: Sita Benedict, UH-Manoa

Title: The modulus of curve families in R^n and its properties (Part 1 of 2)

Abstract: This talk will be an introduction to what is the modulus of a curve family, introduced in 1950 by Ahlfors and Beurling and generalized to its current form by Fuglede in 1957. We will define the modulus for curve families in R^n, but the definition makes sense in a general metric measure space. Although the definition is a bit cumbersome, the modulus has some very nice and useful properties, which lead naturally to the definition of quasiconformal mappings and also Newtonian spaces. These are, respectively, generalizations of conformal mappings and Sobelev spaces. We will prove these nice properties of the modulus and also calculate the modulus of certain families of curves.

See Thomas for details

See organizers Rufus, Alan or Robin for details.

Speaker: Chris Nowlin (NSA)

Title: Mathematics at NSA

Abstract: We will discuss career opportunities for mathematicians at the National Security Agency. The speaker will share reflections on his 5-year career, including the application process, the types of problems NSA mathematicians work on, and some of the good and the bad associated with working for NSA. Questions from the audience are encouraged.

Speaker: Jerry Shurman (Reed College)

Title: Lifts and Congruences of Siegel Modular Forms by the Pullback-Genus Method

Abstract: We compute Hecke eigenform bases of spaces of degree 3 Siegel modular forms and Euler factors of the eigenforms, through weight 22. Our method uses the Fourier coefficients of Siegel Eisenstein series, which are fully known and computationally tractable, and Garrett’s decomposition of the pullback of the Eisenstein series through the Witt map. Our results support Miyawaki’s conjectural lift and Katsurada’s theory of congruence neighbors. Some familiarity with classical modular forms will be helpful.

Speaker: Ranjan Bhaduri

Title: Some Musings of a Mathematician about the Hedge Fund Space

Please join us for a informal seminar by UH Manoa alum and Chief Research Officer at Sigma Analysis & Management Ltd, Dr. Ranjan Bhaduri. He will give us some insights into the mathematics of the hedge fund world.

Bring a lunch or snack for this exciting discussion!

Abstract: The hedge fund space has grown into a multi-trillion dollar business, and there are several quantitative and systematic hedge funds in existence. Many mathematical techniques are invoked in the hedge fund industry. This talk gives some insights about some of the mathematics utilized in the hedge fund world and in portfolio construction of multi-manager portfolios. In addition, it gives some nuggets of wisdom to students (both undergraduate and graduate) looking to have success in the business and finance world.