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Mathematics Graduate Minicourse Series

The Graduate Minicourse Series is a collection of multi-lecture minicourses intended to introduce beginning graduate students to the research opportunities available in our programs and to present important professional topics. Each Minicourse will usually consist of one or two one-hour lectures, either in the 4:00 pm Monday time slot or the parallel 4:00 pm Wednesday time slot. Everyone is welcome to attend and students may register for the one-credit courses AMSC 687, MATH 687 or STAT 687 to receive credit for their participation. To receive credit a student must attend at least four minicourses during the year and write a brief one or two page report on each to be submitted to the minicourse coordinator, Prof. N. Ramachandran ( Students wishing to sign up for credit should speak with the minicourse coordinator as to the expectations for their successful participation.

Schedule of Minicourses

Fall 2007, 4:00 pm, MATH 3206
Oct 3
Vadim Kaloshin
On relative equilibria for the Newtonian N body problem and conjectures of Smale and Saari.
Oct 10
Vadim Kaloshin
On density of collisions and syzygies conjectures for the Newtonian 3 body problem.

Oct 17
Radu Balan
Nonlinear Signal Reconstruction: Moving beyond Linear Transformations and Left Inverses
Oct 24
Radu Balan
Stochastic Modeling in Wireless Local Area Networks

Spring 2007, 4:00pm, MATH3206
March 12
Leonid Koralov

An Introduction to Stochastic Integrals and the Ito Formula, with Applications.

(Time change due to a faculty meeting: 4:30pm- 5:30pm)

Abstract: We'll motivate the notion of the stochastic integral, sketch the proof of the existence of the Brownian Motion, and discuss Ito's formula. We'll then use Ito's formula to describe the long-time behavior of a particle in a random flow.

Apr 9
Harry Tamvakis
From linear algebra and puzzles to quantum cohomology

(Time change due to a faculty meeting: 4:30pm- 5:30pm)

The cohomology ring of the Grassmannian has been studied for well over a century, but in recent years there have been surprising twists to the story. In my first talk I will use only linear algebra to construct this ring from scratch and then describe the beautiful puzzle rule of Knutson-Tao-Woodward for computing the product of two basis elements in the ring (the so-called Schubert classes). We will conclude with a conjectural extension of this rule to the quantum cohomology of the same space. My second talk will combine geometry, topology, and representation theory to compute a complicated but elementary sum of rational functions; again the Grassmannian will play a central role. The techniques I will discuss have wide applications of great importance, for instance in the computation of intersection numbers over the moduli space of Riemann surfaces, or more generally, of Gromov-Witten invariants.

Apr 16
Harry Tamvakis
"How to get a PhD by evaluating a finite sum"

(Time change due to a faculty meeting: 4:30pm- 5:30pm)

Apr 23
Leonid Koralov
Introduction to stochastic calculus, continued
May 7 Wojciech Czaja Mathematics behind signal processing

We shall discuss several aspects of Time-Scale analysis, including discrete and continuous wavelet transforms, and their generalizations. We will also present a possible path for merging Time-Frequency and Time-Scale analysis.

Fall 2006, 4:00 pm, MATH3206
Oct 9
Math 695 TA Teaching seminar
Oct 16
Bulent Atalay (U of Mary Washington)
Leonardo da Vinci and the Mathematics of Aesthetics
Oct 18
Dionisios Margetis
Mathematical modeling I: From physics-based discrete schemes to PDE's and moving-boundary problems
(Time change due to a faculty meeting: 4:30pm- 5:30pm)
Oct 30
Kasso Okoudjou Introduction to analysis on fractals
Nov 6
Kasso Okoudjou Introduction to analysis on fractals, Part II
Nov 13
Math 695 TA Teaching seminar
Nov 15
Dionisios Margetis Mathematical modeling II: Aspects of computing from the perspective of Schrodinger's PDE
Nov 20
Wojciech Czaja
Mathematics behind signal processing I
Nov 27 Wojciech Czaja Mathematics behind signal processing II
Nov 29 Laura Taalman (James Madison Univ) Mathematics of Sudoku (Starts at 4:30pm due to a committee meeting)
Dec 4 Math 695 TA seminar meeting