The Ohio State University

Time

Nov 16 2009 - 4:30pm - 5:30 pm

Location

CH 240

Speaker

James Cogdell (OSU)

Abstract

L-functions are very interesting, and equally mysterious, complex analytic invariants attached to certain arithmetic objects, geometric objects, and analytic objects. L-functions seem to have a wonderful ability to interpolate from the local to the global. The paradigm of an L-function is the Riemann zeta function and the arithmetic contained in it, such as the prime number theorem. Most of our understanding and expectations of L-functions come from examples.

In these two talks I hope to give a feeling for what L-functions are and some of the things we expect from them by discussing several examples, including the Riemann zeta function, the Dirichlet L-functions, the L-function of an elliptic curve, and perhaps Artin L-functions. I will also discuss the analytic side, so L-functions attached to modular or automorphic forms. If there is time, perhaps I may even be able to give a small introduction to the Langlands program.

Notes

This lecture is part of Invitation to Mathematics.
Pre-candidacy students can sign up for this lecture series by registering for one credit hour of Math 693, Call # 27103 (with Prof H. Moscovici).

Time

Nov 9 2009 - 4:30pm - 5:30 pm

Location

CH 240

Speaker

Ching-Shan Chou (OSU)

Abstract

Differential equations and numerical simulation have been widely used in modeling biological systems. In this talk, I will introduce two biological systems related to cell signaling:

• morphological changes of cells under chemical stimuli
• stratification of stem and progenitor cells in an epithelium and the feedback regulation.

Those systems involve very complicated signaling pathways, and I will show how analysis and simulations will be used to investigate those systems.

Notes

This lecture is part of Invitation to Mathematics.
Pre-candidacy students can sign up for this lecture series by registering for one credit hour of Math 693, Call # 27103 (with Prof H. Moscovici).

Time

Oct 26 2009 - 4:30pm - 5:30 pm

Location

CH 240

Speaker

Hsian-Hua Tseng (OSU)

Abstract

Hurwitz numbers are certain combinatorial quantities that admit several different-looking definitions. One way to define Hurwitz numbers is to say that the are counts of covers of the Riemann sphere with specific ramifications. Hurwitz numbers are related to various different areas of mathematics, such as moduli theory and integrable systems. In this talk I will attempt to discuss some of the definitions of Hurwitz numbers, and outline the connections to other areas.

Notes

This lecture is part of Invitation to Mathematics.
Pre-candidacy students can sign up for this lecture series by registering for one credit hour of Math 693, Call # 27103 (with Prof H. Moscovici).

Time

Oct 12 2009 - 4:30pm - 5:30 pm

Location

CH 240

Speaker

Barbara Lee Keyfitz (OSU)

Abstract

A significant difficulty in extending the theory of hyperbolic conservation laws beyond a single space dimension is identifying the singularities in solutions that may appear in multidimensional problems.

Recent numerical results have suggested that even within the much more restricted set of self-similar solutions there may be phenomena that are very complicated indeed -- apparently well beyond the reach of current analysis.

However, while searching for a simple prototype, I have come across a problem that is simple and natural. It appears to have something new to say even about the classical problem of steady transonic flow, and the solution uses the familiar tools named in the title.

The problem and its solution will be expounded in two talks, to an audience that is not assumed to have any prior acquaintance with the theory of conservation laws.

Notes

This lecture is part of Invitation to Mathematics.
Pre-candidacy students can sign up for this lecture series by registering for one credit hour of Math 693, Call # 27103 (with Prof H. Moscovici).

Time

Sep 28 2009 - 4:30pm - 5:30 pm

Location

CH 240

Speaker

Dan Burghelea (OSU)

Abstract

In these days both engineering and experimental sciences collect and store an enormous amount of data whose magnitude makes more and more difficult to reveal the qualitative (and even some quantitative) features. Topology and geometry seems to provide help.

I will explain:

• Why and how Data Analysis might benefit from topology .
• What sort new concepts and new invariants in topology were inspired by data Analysis.

The concept of "persistence" will be the key illustration.

Notes

This lecture is part of Invitation to Mathematics.
Pre-candidacy students can sign up for this lecture series by registering for one credit hour of Math 693, Call # 27103 (with Prof H. Moscovici).

Time

Jun 1 2009 - 4:30pm - 5:30 pm

Location

CH 240

Speaker

David Ralston (OSU)

Abstract

Beginning with nothing more complicated than rotating some starting point x by some irrational rotation α, we can try to find those times n so that of the first n iterates of x under the rotation, exactly half have landed in the bottom half of the circle, and exactly half have landed in the top half.

Abstract results in ergodic theory tell us that the set of such n will generally be infinite but "sparse," in some sense. We can investigate the sparseness by trying to sum 1/n over this set, and seeing if we can expect to form a convergent or divergent series.

Notes

This lecture is part of Invitation to Mathematics.
Pre-candidacy students can sign up for this lecture series by registering for one credit hour of Math 693A, Call # 22463-7 (with H. Moscovici).