Seminars and Colloquia by Series

Wednesday, March 12, 2014 - 12:00 , Location: Skiles 005 , Dr. Sal Barone , School of math , Organizer:
We will discuss a few introductory results in real algebraic geometry concerning semi-algebraic sets. A semi-algebraic subset of R^k is the set of solutions of a boolean combination of finitely many real polynomial equalities and inequalities. These sets arise naturally in many areas of mathematics as well as other scientific disciplines, such as discrete and computational geometry or the configuration spaces in robotic motion planning. After providing some basic definitions and examples, we will outline the proof of a fundamental result, the Oleinik-Petrovsky-Thom-Milnor bound of d(2d-1)^{k-1} on the sum of the Betti numbers of a real algebraic variety, as well as indicate the direction of recent and ongoing research generalizing this result.
Wednesday, March 5, 2014 - 12:00 , Location: Skiles 005 , Dr. Bickel , School of Math , Organizer:
The classic Pick Interpolation Problem asks: Given points z_1, z_n and w_1, w_n in the unit disk, is there a function f(z) that (1) is holomorphic on the unit disk, (2) satisfies f(z_i)=w_i, and (3) satisfies |f(z)|=1 In 1917, Pick showed that such a function f(z) exists precisely when an associated matrix is positive semidefinite. In this talk, I will translate the Pick problem to the language of Hilbert function spaces and present a more modern proof of the Pick problem. The benefit of this approach is that, as shown by J. Agler in 1989, it generalizes easily to the two-variable setting. At the heart of the proof is a method of representing bounded analytic one and two-variable functions using Hilbert space operators. Time-permitting, I will discuss recent results concerning the structure of such representations for bounded two-variable analytic functions, which is joint work with G. Knese.
Wednesday, February 26, 2014 - 12:00 , Location: Skiles 005 , Dr. Plamen Iliev , School of Math , Organizer:
Hypergeometric functions have played an important role in mathematics and physics in the last centuries. Multivariate extensions of the classical hypergeometric functions have appeared recently in different applications. I will discuss research problems which relate these functions to the representation theory of Lie algebras and quantum superintegrable systems.
Wednesday, February 19, 2014 - 12:00 , Location: Skiles 005 , Dr. Zhou , School of Math , Organizer:
Abstract: In this talk, I will use two examples, the influence prediction in social media, and the short path in engineering, to illustrate how we use differential equations to establish models for problems in social science and engineering, and how to use mathematics to design efficient algorithms to compute the solutions. The talk is mainly for first or second year graduate students, and it is based on collaborative work with several faculty members and graduate students in SoM, ECE, CoC.
Wednesday, February 12, 2014 - 12:00 , Location: Skiles 005 , Prof. Kang , School of Math , Organizer:
This talk is an introduction to mathematical approaches to image processing: using variational approaches and PDE based method. Various problems and a few different approaches will be introduced.
Wednesday, February 5, 2014 - 12:00 , Location: Skiles 005 , Dr. Henry Matzinger , School of Mathematics , Organizer:
We present several main models in this area including random polymers. We then explain some open problems big and small as well as a few of our related results.
Wednesday, January 22, 2014 - 12:00 , Location: Skiles 005 , Dr. Lacey , School of Math , Organizer:
Beginning with the Cauchy formula, we introduce the Poisson average, and the Carleson embeding theorem. From there, recent weighted estimates for the Hilbert and Cauchy transforms can be introduced.
Wednesday, January 15, 2014 - 12:00 , Location: Skiles 005 , Dr. Joe Rabinoff , School of Math , Organizer:
The theory of non-Archimedean analytic spaces closely parallels that of complex analytic spaces, with many theorems holding in both situations. I'll illustrate this principle by giving a survey of the structure theory of analytic curves over non-Archimedean fields, and comparing them to classical Riemann surfaces. I'll draw plenty of pictures and discuss topology, pair-of-pants decompositions, etc.
Wednesday, December 4, 2013 - 12:00 , Location: Skiles 005 , Dr. Tom Trotter , School of Math , Organizer:
Answering a question of R. Stanley, we show that for each t ≥1, there is a least positive integer f(t) so that a planar poset with t minimal elements has dimension at most f(t). In particular, we show that f(t) ≤ 2t + 1 and that this inequality is tight for t=1 and t=2. For larger values of t, we can only show that f(t) ≥ t+3. This research is joint work with Georgia Tech graduate student Ruidong Wang.
Wednesday, November 20, 2013 - 12:00 , Location: Skiles 005 , Dr. Stavros Garoufalidis , School of Math , , Organizer:
Hyperbolic 3-manifolds is a great class of 3-dimensional geometric objects with interesting topology, a rich source of examples (practially one for every knot that you can draw), with arithmetically interesting volumes expressed in terms of dialogarithms of algebraic numbers, and with computer software that allows to manipulate them. Tired of abstract existential mathematics? Interested in concrete 3-dimensional topology and geometry? Or maybe Quantum Topology? Come and listen!