Department of Mathematics

Calendar


Next Week

Department of Mathematics Colloquium, Michel Chipot, University of Zurich, MATH 175

Tuesday, September 2, 2014, 4:30 - 5:30 PM EDT

Asymptotic Issues

Abstract: We would like to present some results on the asymptotic behaviour of different problems set in cylindrical domains of the type $\ell\omega_1 \times \omega_2$ when $\ell\to\infty$. For $i = 1, 2 \omega_i$ are two bounded open subsets in $\Bbb R^{d_i}$. To fix the ideas on a simple example consider for instance $\omega_1 = \omega_2 = (-1,1)$ and $u_\ell$ the solution to $$ -\Delta u_\ell = f\ in\ \Omega_\ell = (-\ell,\ell) \times (-1,1), u_\ell = 0 \ on\ \partial\Omega_\ell. $$ It is more or less clear that, when $\ell\to\infty$, $u_\ell$ will converge toward $u_\infty$ solution to $$ -\Delta u_\infty = f \ in\ \Omega_\infty = (-\infty,\infty) \times (-1,1), u_\infty = 0 \ on\ \partial\Omega_\infty. $$ However this problem has infinitely many solutions since for every integer k $$ exp(k\pi x_1)sin(k\pi x_2) $$ is solution of the corresponding homogeneous problem. Our goal is to explain the selection process of the solution for different problems of this type when $\ell\to\infty$. Refreshments will be served in the Math Library Lounge at 4:00 p.m.

Commutative Algebra Seminar, Professor Giulio Caviglia, Purdue University, UNIV 119

Wednesday, September 3, 2014, 2:30 - 3:30 PM EDT

Zero-generic Initial Ideals

Algebraic Geometry Seminar, Kenji Matsuki, Purdue University, MATH 731

Wednesday, September 3, 2014, 3:30 - 4:30 PM EDT

A new strategy for resolution of singularities in the monomial case in positive characteristic

Abstract: According to our approach for resolution of singularities in positive characteristic (called the Idealistic Filtration Program, alias the I.F.P. for short) the algorithm is divided into the following two steps: Step 1. Reduction of the general case to the monomial case. Step 2. Solution in the monomial case. While we have established Step 1 in arbitrary dimension, Step 2 becomes very subtle and difficult in positive characteristic. In dimension 3, we provided an invariant, inspired by the work of Benito-Villamayor, which establishes Step 2. In this talk, we propose a new strategy to settle the monomial case, and provide a different invariant in dimension 3 based upon this strategy. The new invariant increases from time to time (the well-known Moh-Hauser jumping phonomena), while it is then shown to eventually decrease. (The analysis of the eventual decrease in our monomial case is done without any restriction on the power of the leading term of the monic equation involved, extending the analysis done by Hauser.) Since the old invariant strictly decreases after each transformation, this may look like a step backward rather than forward. However, the construction of the new invariant is more faithful to the original philosophy of Villamayor, and we believe that the new strategy has a better fighting chance in higher dimensions.

Student Colloquium, Mr. Andrew Ursitti, Purdue University, UNIV 017

Wednesday, September 3, 2014, 4:30 - 5:30 PM EDT

The Real Numbers as a Wreath Product

Abstract: The title of the lecture is the title of a 1975 article in Advances in Mathematics by Faltin, Metropolis, Ross, and Rota, in which the authors give a completely algebraic construction of the real numbers. In this lecture I will present this construction and a similar construction of the p-adic numbers.

Probability Seminar, Yankeng Luo, Purdue University, UNIV 103

Thursday, September 4, 2014, 3:30 - 4:30 PM EDT

Basic Notions Seminar, Steve Bell, Purdue University, BRNG B222

Friday, September 5, 2014, 3:30 - 4:30 PM EDT

The Amazing Bergman Kernel

Abstract: It's amazing how an abstractly defined object like the Bergman kernel connects geometry to analysis to algebra. I will explain what the Bergman kernel is and what it does.


Two Weeks

Department of Mathematics Colloquium, Sasha Voronov, University of Minnesota, MATH 175

Tuesday, September 9, 2014, 4:30 - 5:30 PM EDT

Classical and Quantum Master Equations

Abstract: The Maurer-Cartan equation d w + [w,w]/2 = 0, known in geometry as the condition for the vanishing of the curvature of a connection given by a Lie-algebra valued 1-form w, is also an important equation in deformation theory as well as in quantum field theory, where it is called the Classical Master Equation (CME). Physicists have also been using a quantized version, dw + h \Delta w + {w,w}/2, which they call the Quantum Master Equation (QME). We will review how the CME is used in deformation theory and give a geometric interpretation of solutions of the Classical and Quantum Master Equations. Refreshments will be served in the Math Library Lounge at 4:00 p.m.

Probability Seminar, Krzysztof Bogdan, Wroclaw University of Technology, UNIV 103

Thursday, September 11, 2014, 3:30 - 4:30 PM EDT


Three Weeks

Probability Seminar, UNIV 103

Thursday, September 18, 2014, 3:30 - 4:30 PM EDT


September

Probability Seminar, UNIV 103

Thursday, September 25, 2014, 3:30 - 4:30 PM EDT

Jean Rubin Memorial Lecture, Margaret Cheney, Colorado State University, MATH 175

Tuesday, September 30, 2014, 4:30 - 5:30 PM EDT

TBA

Refreshments will be served in the Math Library Lounge at 4:00 p.m.


October

Probability Seminar, UNIV 103

Thursday, October 2, 2014, 3:30 - 4:30 PM EDT

Computational & Applied Mathematics Colloquium, Professor Mark Ainsworth, Brown University, REC 122

Monday, October 6, 2014, 3:30 - 4:30 PM EDT

TBA

Department of Mathematics Colloquium, Alejandro Adem, University of British Columbia, MATH 175

Tuesday, October 7, 2014, 4:30 - 5:30 PM EDT

TBA

Refreshments will be served in the Math Library Lounge at 4:00 p.m.

Probability Seminar, UNIV 103

Thursday, October 9, 2014, 3:30 - 4:30 PM EDT

Probability Seminar, UNIV 103

Thursday, October 16, 2014, 3:30 - 4:30 PM EDT

Department of Mathematics Colloquium, Jonathan Rosenberg, University of Maryland, MATH 175

Tuesday, October 21, 2014, 4:30 - 5:30 PM EDT

TBA

Refreshments will be served in the Math Library Lounge at 4:00 p.m.

Probability Seminar, UNIV 103

Thursday, October 23, 2014, 3:30 - 4:30 PM EDT

Computational & Applied Mathematics Seminar, Dr. Wujun Zhang, University of Maryland, REC 122

Monday, October 27, 2014, 3:30 - 4:30 PM EDT

TBA

Department of Mathematics Colloquium, Francis Bonahon, University of Southern California, MATH 175

Tuesday, October 28, 2014, 4:30 - 5:30 PM EDT

TBA

Refreshments will be served in the Math Library Lounge at 4:00 p.m.

Probability Seminar, UNIV 103

Thursday, October 30, 2014, 3:30 - 4:30 PM EDT


November

Department of Mathematics Colloquium, Jean Bellissard, Georgia Tech, MATH 175

Tuesday, November 4, 2014, 4:30 - 5:30 PM EST

TBA

Refreshments will be served in the Math Library Lounge at 4:00 p.m.

Probability Seminar, Camelia Pop, University of Pennsylvania, UNIV 103

Thursday, November 6, 2014, 3:30 - 4:30 PM EST

Department of Mathematics Colloquium, Justin Moore, Cornell, MATH 175

Tuesday, November 11, 2014, 4:30 - 5:30 PM EST

TBA

Refreshments will be served in the Math Library Lounge at 4:00 p.m.

Probability Seminar, Daniel Kelleher, Purdue University, UNIV 103

Thursday, November 13, 2014, 3:30 - 4:30 PM EST

Probability Seminar, UNIV 103

Thursday, November 20, 2014, 3:30 - 4:30 PM EST


December

Probability Seminar, UNIV 103

Thursday, December 4, 2014, 3:30 - 4:30 PM EST

Probability Seminar, UNIV 103

Thursday, December 11, 2014, 3:30 - 4:30 PM EST


2015

Computational & Applied Mathematics Seminar, Professor Alina Chertock, North Carolina State University, REC 122

Monday, January 26, 2015, 3:30 - 4:30 AM EST

TBA