Colloquia 2012-2013

Mathematics Colloquium

All colloquia are on Fridays at 4:00 pm in Van Vleck B239, unless otherwise indicated.

Spring 2012

date	speaker	title	host(s)
Jan 23, 4pm	Saverio Spagnolie (Brown)	Hydrodynamics of Self-Propulsion Near a Boundary: Construction of a Numerical and Asymptotic Toolbox	Jean-Luc
Jan 27	Ari Stern (UCSD)	Numerical analysis beyond Flatland: semilinear PDEs and problems on manifolds	Jean-Luc / Julie
Feb 3	Akos Magyar (UBC)	On prime solutions to linear and quadratic equations	Street
Feb 8	Lan-Hsuan Huang (Columbia U)	Positive mass theorems and scalar curvature problems	Sean
Feb 10	Melanie Wood (UW Madison)	Counting polynomials and motivic stabilization	local
Feb 17	Milena Hering (University of Connecticut)	The moduli space of points on the projective line and quadratic Groebner bases	Andrei
Feb 24	Malabika Pramanik (University of British Columbia)	TBA	Benguria
March 2	Guang Gong (Electrical Engineering, University of Waterloo)	Polyphase Sequence Families with Low Correlation and DFT for Spreading OFDM	Shamgar
March 16	Charles Doran (University of Alberta)	TBA	Matt Ballard
March 19	Colin Adams and Thomas Garrity (Williams College)	Which is better, the derivative or the integral?	Maxim
March 23	Martin Lorenz (Temple University)	TBA	Don Passman
March 30	Wilhelm Schlag (University of Chicago)	TBA	Street
April 6	Spring recess
April 13	Ricardo Cortez (Tulane)	TBA	Mitchell
April 18	Benedict H. Gross (Harvard)	TBA	distinguished lecturer
April 19	Benedict H. Gross (Harvard)	TBA	distinguished lecturer
April 20	Robert Guralnick (University of Southern California)	TBA	Shamgar
April 27	Gui-Qiang Chen (Oxford)	TBA	Feldman
May 4	Mark Andrea de Cataldo (Stony Brook)	TBA	Maxim
May 11	Tentatively Scheduled		Shamgar

Abstracts

Mon, Jan 23: Saverio Spagnolie (Brown)

"Hydrodynamics of Self-Propulsion Near a Boundary: Construction of a Numerical and Asymptotic Toolbox"

The swimming kinematics and trajectories of many microorganisms are altered by the presence of nearby boundaries, be they solid or deformable, and often in perplexing fashion. When an organism's swimming dynamics vary near such boundaries a question arises naturally: is the change in behavior fluid mechanical, biological, or perhaps due to other physical laws? We isolate the first possibility by exploring a far-field description of swimming organisms, providing a general framework for studying the fluid-mediated modifications to swimming trajectories. Using the simplified model we consider trapped/escape trajectories and equilibria for model organisms of varying shape and propulsive activity. This framework may help to explain surprising behaviors observed in the swimming of many microorganisms and synthetic micro-swimmers. Along the way, we will discuss the numerical tools constructed to analyze the problem of current interest, but which have considerable potential for more general applicability.

Fri, Feb 3: Akos Magyar (UBC)

On prime solutions to linear and quadratic equations

The classical results of Vinogradov and Hua establishes prime solutions of linear and diagonal quadratic equations in sufficiently many variables. In the linear case there has been a remarkable progress over the past few years by introducing ideas from additive combinatorics. We will discuss some of the key ideas, as well as their use to obtain multidimensional extensions of the theorem of Green and Tao on arithmetic progressions in the primes. We will also discuss some new results on prime solutions to non-diagonal quadratic equations of sufficiently large rank. Most of this is joint work with B. Cook.

Wed, Feb 8: Lan-Hsuan Huang (Columbia U)

Positive mass theorems and scalar curvature problems

More than 30 years ago, Schoen-Yau and later Witten made major breakthroughs in proving the positive mass theorem. It has become one of the most important theorems in general relativity and differential geometry. In the first part of the talk, I will introduce the positive mass theorem and present our recent work that extends the classical three-dimensional results to higher dimensions. In the second part, I will discuss how the observation from general relativity enables us to solve classical geometric problems related to the scalar curvature.

Fri, Feb 10: Melanie Wood (local)

Counting polynomials and motivic stabilization

We will begin with the problem of counting polynomials modulo a prime p with a given pattern of root multiplicity. Here we will discover phenomena that point to vastly more general patterns in configuration spaces of points. To see these patterns, one has to work in the ring of motives--so we will describe this place where a space is equivalent to the sum of its pieces. We will then be able to describe how these patterns in the ring of motives are related to theorems in topology on the homological stability of configuration spaces. This talk is based on joint work with Ravi Vakil.

Fri, Feb. 17: Milena Hering (UConn)

The moduli space of points on the projective line and quadratic Groebner bases

The ring of invariants for the action of the automorphism group of the projective line on the n-fold product of the projective line is a classical object of study. The generators of this ring were determined by Kempe in the 19th century. However, the ideal of relations has been only understood recently in work of Howard, Millson, Snowden and Vakil. They prove that the ideal of relations is generated by quadratic equations using a degeneration to a toric variety. I will report on joint work with Benjamin Howard where we further study the toric varieties arising in this degeneration. As an application we show that the second Veronese subring of the ring of invariants admits a presentation whose ideal admits a quadratic Groebner basis.

Fri, Feb. 24: Malabika Pramanik (UBC)

Analysis on Sparse Sets

Abstract

Fri, March 2: Guang Gong (Department of EE University of Waterloo)

Polyphase Sequence Families with Low Correlation and DFT for Spreading OFDM

Spreading sequences are employed for providing frequency diversity for an orthogonal frequency division multiplexing (OFDM) system and relieving its high peak power. In this talk, I will present the current status of the constructions of polyphase sequences and sequence families with low correlation and discrete Fourier transform (DFT) spectrum or large zero correlation zone and their applications in the spreading OFDM system. I will first introduce different constructions for those polyphase sequence families. Then I present some of our recent work on power residue sequences, Sidelnikov sequences, the Weil representation sequences, and new sequences with low correlation and DFT which can be obtained by directly using the Weil bounds, together with the shift-and-add method for increasing the sizes of the sequence families with a graceful degrading correlation and DFT. Following this, I show our new findings on the Golay sequences with large zero autocorrelation zones. Finally, I will conclude my talk by exhibiting some unsolved problems along this line and some experimental results in the applications of spreading OFDM systems with these aforementioned sequences.