Department of Mathematics
http://as.vanderbilt.edu/math
College of Arts and Science | Vanderbilt UniversityFri, 30 Sep 2016 21:10:49 +0000enhourly1http://wordpress.org/?v=3.1.4Seiberg-Witten Theory and Geometry of 4-Manifolds
http://as.vanderbilt.edu/math/2016/09/seiberg-witten-theory-and-geometry-of-4-manifolds/
http://as.vanderbilt.edu/math/2016/09/seiberg-witten-theory-and-geometry-of-4-manifolds/#commentsFri, 30 Sep 2016 21:10:49 +0000pam.joneshttp://as.vanderbilt.edu/math/?p=3917The Seiberg-Witten theory provides a smooth invariant, which can be used to distinguish homeomorphic, non-diffeomorphic, smooth structures. It also has a deep impact on the Riemannian properties of 4-manifolds. We will discuss how obstructions to the existence of Einstein metrics arise, and how one can compute the Yamabe invariant for Kahler surfaces and some symplectic 4-manifolds.
]]>http://as.vanderbilt.edu/math/2016/09/seiberg-witten-theory-and-geometry-of-4-manifolds/feed/0Graduate Student Tea
http://as.vanderbilt.edu/math/2016/09/graduate-student-tea-53/
http://as.vanderbilt.edu/math/2016/09/graduate-student-tea-53/#commentsWed, 28 Sep 2016 20:30:49 +0000pam.joneshttp://as.vanderbilt.edu/math/?p=3913http://as.vanderbilt.edu/math/2016/09/graduate-student-tea-53/feed/0Polynomial Metric Spaces and Minimal Energy
http://as.vanderbilt.edu/math/2016/09/polynomial-metric-spaces-and-minimal-energy/
http://as.vanderbilt.edu/math/2016/09/polynomial-metric-spaces-and-minimal-energy/#commentsWed, 28 Sep 2016 20:00:19 +0000pam.joneshttp://as.vanderbilt.edu/math/?p=3946http://as.vanderbilt.edu/math/2016/09/polynomial-metric-spaces-and-minimal-energy/feed/0The Twisted Nature of Polyominoes
http://as.vanderbilt.edu/math/2016/09/the-twisted-nature-of-polyominoes/
http://as.vanderbilt.edu/math/2016/09/the-twisted-nature-of-polyominoes/#commentsWed, 28 Sep 2016 00:00:28 +0000pam.joneshttp://as.vanderbilt.edu/math/?p=3915Polyominoes are flat geometric figures obtained by joining several equal squares edge to edge. They can tile the plane, help you play Tetris or Blokus, serve as a literary subject or a test case for your programming/counting skills, or simply be the building blocks of many a joyous pastime. But for all that flatness, there’s a certain twist to them. (Pizza and drinks will be provided.)
]]>http://as.vanderbilt.edu/math/2016/09/the-twisted-nature-of-polyominoes/feed/0Universal Partial Words
http://as.vanderbilt.edu/math/2016/09/universal-partial-words/
http://as.vanderbilt.edu/math/2016/09/universal-partial-words/#commentsMon, 26 Sep 2016 21:10:32 +0000pam.joneshttp://as.vanderbilt.edu/math/?p=3925Given an alphabet A, we say a word over A is a universal word (often called a De Bruijn sequence) for A^n if each word over A of length n appears in it exactly once. De Bruijn showed in 1946 that these exist for all finite alphabets and all n. Recently, the following generalization of these words was introduced. A universal partial word w for A^n again must cover each word over A exactly once, but w is allowed to include the wildcard character, which counts as all characters of A. In particular, our recent work primarily looks at the case when A is not a binary alphabet.
]]>http://as.vanderbilt.edu/math/2016/09/universal-partial-words/feed/0New Variational Principles, Convexity and Supercritical Semi-Linear Elliptic Problems
http://as.vanderbilt.edu/math/2016/09/new-variational-principles-convexity-and-supercritical-semi-linear-elliptic-problems/
http://as.vanderbilt.edu/math/2016/09/new-variational-principles-convexity-and-supercritical-semi-linear-elliptic-problems/#commentsFri, 23 Sep 2016 22:10:58 +0000pam.joneshttp://as.vanderbilt.edu/math/?p=3880The object of this talk is to present new variational principles for certain differential equations. These principles provide new representations and formulations for the superposition of the gradient of convex functions and symmetric operators. They yield new variational resolutions for a large class of hamiltonian partial differential equations with variety of linear and nonlinear boundary conditions including many of the standard ones. This approach seems to offer several useful advantages: It associates to a boundary value problem several potential functions which can often be used with relative ease compared to other methods such as the use of Euler-Lagrange functions. These potential functions are quite flexible, and can be adapted to easily deal with both nonlinear and homogeneous boundary value problems. Additionally, in some cases, this new method allows dealing with problems beyond the usual locally compactness structure (problems with a supercritical Sobolev nonlinearity).
]]>http://as.vanderbilt.edu/math/2016/09/new-variational-principles-convexity-and-supercritical-semi-linear-elliptic-problems/feed/0Talk Title TBA
http://as.vanderbilt.edu/math/2016/09/talk-title-tba-132/
http://as.vanderbilt.edu/math/2016/09/talk-title-tba-132/#commentsFri, 23 Sep 2016 22:10:06 +0000pam.joneshttp://as.vanderbilt.edu/math/?p=3826http://as.vanderbilt.edu/math/2016/09/talk-title-tba-132/feed/0Waldhausen’s Algebraic K-Theory
http://as.vanderbilt.edu/math/2016/09/waldhausens-algebraic-k-theory/
http://as.vanderbilt.edu/math/2016/09/waldhausens-algebraic-k-theory/#commentsFri, 23 Sep 2016 21:10:07 +0000pam.joneshttp://as.vanderbilt.edu/math/?p=3905In preparation for my talk next week, I’ll introduce algebraic K-theory. In particular, I’ll introduce a formulation due to Waldhausen, which is the most general version of the algebraic K-theory machine. I’ll discuss some examples, and discuss some places of interest where this machine fails to work (which I will discuss in the next talk). The talk will require no previous knowledge of algebraic K-theory.
]]>http://as.vanderbilt.edu/math/2016/09/waldhausens-algebraic-k-theory/feed/0The Sphere Packing Problem in Dimensions 8 and 24
http://as.vanderbilt.edu/math/2016/09/talk-title-tba-113/
http://as.vanderbilt.edu/math/2016/09/talk-title-tba-113/#commentsThu, 22 Sep 2016 22:10:42 +0000rongiolhttp://as.vanderbilt.edu/math/?p=3657The sphere packing problem is to find an arrangement of non-overlapping unit spheres in the d-dimensional Euclidean space in which the spheres fill as large a proportion of the space as possible. In this talk we will present a solution of the sphere packing problem in dimensions 8 and 24. In 2003 N. Elkies and H. Cohn proved that the existence of a real function satisfying certain constrains leads to an upper bound for the sphere packing constant. Using this method they obtained almost sharp estimates in dimensions 8 and 24. We will show that functions providing exact bounds can be constructed explicitly as certain integral transforms of modular forms. Therefore, the sphere packing problem in dimensions 8 and 24 is solved by a linear programming method. Tea at 3:30 pm in SC 1425. (Contact Person: Ed Saff)
]]>http://as.vanderbilt.edu/math/2016/09/talk-title-tba-113/feed/0Talk Title TBA
http://as.vanderbilt.edu/math/2016/09/talk-title-tba-127/
http://as.vanderbilt.edu/math/2016/09/talk-title-tba-127/#commentsWed, 21 Sep 2016 22:10:03 +0000rongiolhttp://as.vanderbilt.edu/math/?p=3756http://as.vanderbilt.edu/math/2016/09/talk-title-tba-127/feed/0