Mathematics Seminars




April 25, Wednesday, 3:30 pm; Seminar Hall

Speaker:   Abhik Ganguli
Title:         Mod p reduction of certain p-adic Galois representations
Abstract:   This talk will be an overview of some local methods giving the modulo p reduction of certain p-adic Galois representations. When the Galois representations associated to certain modular forms are crystalline at p, techniques such as from p-adic Hodge theory can be employed to compute the reductions in the small weight range.

April 20, Friday, 3:30 pm; Seminar Hall

Speaker:   Tom Farrell, Binghamton University
Title:         Introduction to topological rigidity
Abstract:   Mostow proved that n-dimensional closed (compact with empty boundary) Riemannian manifolds M and N with constant -1 sectional curvatures and isomorphic fundamental groups are isometric when n>2. In the more general setting where the sectional curvatures are negative but not necessarily constant, isometry is clearly too much to expect. But diffeomorphism or at least homeomorphism seemed plausible. I will discuss why homeomorphism is true when n>4. This is joint work with Lowell Jones.

April 18, Wednesday, 3:30 pm; Seminar Hall

Speaker:   Varadharaj Srinivasan
Title:         Liouvillian extensions and the Galois theory of linear differential equations
Abstract:  Click here 

March 28, Wednesday, 3:30 pm; Seminar Hall

Speaker:   Rajeeva Karandikar, Chennai Mathematical Institute
Title:         Is there a science behind opinion polls?
Abstract:   Is there a science behind opinion polls? How can obtaining opinion of, say 30,000 voters be sufficient to predict the outcome in a country with over 70 Crore voters? We will address such questions and show that simple mathematics and statistics, lots of common sense and a good understanding of the ground reality or domain knowledge together can yield very good forecast or predictions of the outcome of elections based on opinion polls and exit polls. I will share my own experiences with opinion polls and exit polls over last 14 years.

March 20, Tuesday, 3:30 pm; Seminar Hall

Speaker:   Christophe Mourougane, University of Rennes, France
Title:        Sections of families of hypersurfaces of large degree.
Abstract:   As an answer to Mordell problem over function fields, Grauert and Manin showed that a non-isotrivial algebraic family of compact complex hyperbolic curves has finitely many sections. We consider a generic moving enough family of high enough degree hypersurfaces in a complex projective space. We show the existence of a strict closed subset of its total space that contains the image of all its sections.

March 16, Friday, 2 pm; Seminar Hall

Speaker:  Sylvia Wiegand, University of Nebraska
Title:        Prime ideals in Noetherian rings.
Abstract:  Let R be a commutative Noetherian ring. We consider the set Spec(R) of prime ideals of R as a partially ordered set, ordered by inclusion. Around 1950 Irving Kaplansky asked, "Which partially ordered sets arise as Spec(R) for some Noetherian ring R?" This question is completely open, even if only two-dimensional sets are considered, despite a large amount of work over the intervening years by many mathematicians, such as Hochster, Heitmann, Nagata, McAdam, and Ratliff. In this talk, we describe prime spectra for some two-dimensional rings of polynomials and power series. This involves our work and work of William Heinzer, Roger Wiegand and our students.