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Unless otherwise noted, talks will be at 3:50 PM in O'Connor 104. Also, there will be refreshments before each talk in O'Connor 31 at 3:30 PM.
Tuesday, Oct 21st
Speaker: John Stillwell, University of San Francisco
Title: What Does "Depth" Mean in Math?
Abstract: Every mathematician believes that certain theorems are "deep," but the concept of depth does not have a formal definition. By looking at some famous theorems, ancient and modern, we will
study some candidates for "depth" at various levels, particularly
the undergraduate level. With these examples in hand we hope to
discuss whether any concepts of logic now available can give "depth"
a precise meaning.
Tuesday, Oct 28th
Speaker: Timothy Hsu, San Jose State
Title: Cube complexes, 3-manifolds, and the Virtually Fibered Conjecture
Abstract: Until recently, the Virtual Haken Conjecture was
probably the biggest open problem in 3-manifolds
(3-dimensional geometry). Then, in March 2012, Ian Agol
proved a stronger version, known as the Virtually
Fibered Conjecture, by completing a key part of Dani Wise's
program of studying nonpositively curved cube
complexes. So how were questions in 3-manifolds resolved
using spaces made from high-dimensional cubes? We'll give
an overview explaining the connection and describe the
speaker's joint work with Wise that is part of the emerging
and rapidly growing subject of cube complexes.
Background: One semester of abstract algebra. No topology
required; we will give at least cartoon definitions of the
relevant terms from topology (e.g., 3-manifold).
Tuesday, Nov 11th
Speaker: Gregory Smith, Queen's University
Title: Nonnegative polynomials and sums of squares
Abstract: A polynomial with real coefficients is nonnegative if it takes on only nonnegative values. For example, any sum of squares is obviously nonnegative. For a homogeneous polynomial with respect to the standard grading, Hilbert famously characterized when the converse holds, that is when every nonnegative homogeneous polynomial is a sum of squares. After reviewing some history of this problem, we will examine this converse in more general settings. This line of inquiry has unexpected connections to classical algebraic geometry and leads to new examples in which every nonnegative homogeneous polynomial is a sum of squares. This talk is based on joint work with Grigoriy Blekherman and Mauricio Velasco.
Tuesday, Nov 18th
Speaker: George Mohler, Santa Clara University
*** A Pi Mu Epsilon Sponsored Event
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