UMA Talks 2011-2012

If you'd like to suggest a speaker or a topic for a lecture, email us!

Abstracts for UMA talks from previous years may be found here: 2003-2004, 2004-2005, 2005-2006, 2006-2007, 2007-2008, and 2008-2009.

Fall 2011

Date	Speaker	Title
13 September 2011	Prof. Abhinav Kumar	Spherical Codes and Linear Programming Bounds Abstract: How many points can be placed on a sphere in n dimensions, which are all separated by at least some given distance? This classical problem in discrete geometry involves some beautiful configurations. Professor Kumar will describe a few of these, and also talk about upper bounds for the number of points, which come from linear programming bound and use some representation theory/harmonic analysis. In particular, for some of the more remarkable configurations, we get sharp bounds which prove that they are optimal and even unique. If time permits, Professor Kumar will also talk about similar bounds for potential energy (Thomson's problem).
20 September 2011	Prof. Scott Sherffield	How to Share with Gallants and Boors: A Fun Game Theoretic Puzzle Abstract: Imagine you and a partner sit at a table with k distinct morsels of food (sushi rolls, say) of different types. You take turns selecting morsels until all are eaten. If you and your friend each get different amounts of enjoyment from each different type of food (and these values are commonly known), how will you make your selections if your only goal is to maximize your own enjoyment? What if your only goal is to maximise the enjoyment of your partner? What if there are multiple people, perhaps a mix of greedy and short-sighted souls (boors) and strategists obsessed with the enjoyment of others (gallants), and you know who is who? It turns out that the optimal strategies have a rather nice form. Can you figure it out before talk?
27 September 2011	Prof. Scott Aaronson	The Permanent and the Determinant: The Amazing Role of Two Deceptively-Simple Functions, in Everything From Quantum Mechanics to the P=?NP Problem Abstract: Given an n-by-n matrix, two of the most natural quantities to consider are its permanent and its determinant. But despite the similarity of their definitions, it's been known for decades that these functions differ dramatically in their computational properties: the permanent is #P-complete (i.e., "even harder than NP-complete"), whereas the determinant is computable in polynomial time. In this talk, I'll tell an interconnected story about this pair of functions, touching briefly on some subset of the following (depending on audience interest): -- Why these functions play central roles in Geometric Complexity Theory, Ketan Mulmuley's approach to the P=?NP problem based on algebraic geometry and representation theory -- The two basic types of particle in the universe (bosons and fermions), and how their differences arise from differences between the permanent and determinant functions -- A result of Valiant that free fermion systems can be efficiently simulated by a classical computer, basically because the determinant is in P -- A recent result of myself and Arkhipov showing that free boson systems probably CAN'T be efficiently simulated by a classical computer, basically because the permanent is #P-complete -- How I recently used the connection with bosons to give a new proof that the permanent is #P-complete -- The distribution of the determinants of Gaussian random matrices, and a corresponding open problem for the permanents (Terry Tao couldn't solve this problem, but hopefully one of you can!)
4 October 2011	Prof. James Munkres	What Are Manifolds and Why Do We Study Them?
18 October 2011	Dr. Tanya Khovanova	The Jewish Problem Abstract: She will explain how mathematics was used to discriminate against Jewish people at the entrance exams to the math department of Moscow State University thirty years ago. Many problems had a simple solution that was difficult to find. Such problems protected the administration from extra complaints and appeals. She will give an historical background and discuss a lot of tricky problems that were referred to as "Jewish" or "Coffin" problems. If you want to prepare for the talk, try to formulate in two words the main idea behind a simple solution to the following problem: Find all functions F (x) : R --> R having the property that for any x1 and x2 the following inequality holds: F (x1) - F (x2) < =(x1 - x2)^2

Spring 2012

Date	Speaker	Title
14 February 2012	Prof. Richard Stanley	Pick's Theorem and Beyond Enumerating lattice points in polytopes
28 February 2012	Prof. Jacob Fox	Ramsey Numbers Abstract: Ramsey theory refers to a large body of deep results in mathematics which show that "complete disorder is impossible". I will describe some of the fundamental problems and results in this area, and the recent solution by David Conlon, Benny Sudakov, and myself of an old problem of Paul Erdos on the distribution of monochromatic cliques in 2-edge-colorings of complete graphs.
13 March 2012	Yufei Zhao	Extremal Graph Theory Abstract: This talk will be an introduction to extremal graph theory, a field of mathematics dealing with questions such as, which triangle-free graph on n vertices has the most edges? I will talk about some classical results such as Turan's theorem and their applications to other areas of mathematics. Extremal graph theory is an active research area with many open problems. No background will be assumed for the talk.