Seminar Calendar
for Math 499: Introduction to Graduate Mathematics events the year of Saturday, September 22, 2012.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
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Wednesday, February 1, 2012

Math 499: Introduction to Graduate Mathematics
4:00 pm   in 245 Altgeld Hall,  Wednesday, February 1, 2012
 Del Edit Copy
Submitted by seminar.
 Joseph Rosenblatt (Department of Mathematics, University of Illinois)Averaging over Rectangles in Euclidean Spaces

Wednesday, February 8, 2012

Math 499: Introduction to Graduate Mathematics
4:00 pm   in 245 Altgeld Hall,  Wednesday, February 8, 2012
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Submitted by seminar.
 William Haboush (Department of Mathematics, University of Illinois)What is a root system?

Wednesday, February 15, 2012

Math 499: Introduction to Graduate Mathematics
4:00 pm   in 245 Altgeld Hall,  Wednesday, February 15, 2012
 Del Edit Copy
Submitted by seminar.
 Peter Loeb (Department of Mathematics, University of Illinois)Infinitesimals in Analysis and Probability TheoryAbstract: The notion of an infinitesimal quantity has been used in mathematics for over 2200 years. It eluded rigorous treatment until the work using model theory of Abraham Robinson in 1960 established a rigorous foundation for the use of infinitesimals in mathematics. Recent extensions and applications of his theory, now called nonstandard analysis, have produced new results in many areas including operator theory, stochastic processes, mathematical economics and mathematical physics. In all of these areas, infinitely small and infinitely large quantities can play an essential role in the creative process. At the level of calculus, the integral can now be correctly defined as the nearest ordinary number to an infinitely large sum of infinitesimal quantities. In Probability theory, Brownian motion can now be rigorously parameterized by a random walk with infinitesimal increments. In economics, an ideal economy can be formed from an infinite number of agents each having an infinitesimal influence on the economy. Spaces formed with nonstandard analysis give the simplest probability spaces for a continuum of independent random variables or traders in an economy. The talk gives an introduction to this fruitful area of mathematics.

Wednesday, February 29, 2012

Math 499: Introduction to Graduate Mathematics
4:00 pm   in 245 Altgeld Hall,  Wednesday, February 29, 2012
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Submitted by katz.
 Sheldon Katz   [email] (Department of Mathematics, University of Illinois at Urbana-Champaign)Introduction to Algebraic GeometryAbstract: Illustrating throughout with plane curves, I will give a tour of algebraic geometry, touching on both the classical and the modern. I will also give connections to other areas of study, from elementary calculus to string theory in theoretical physics.

Wednesday, March 14, 2012

Math 499: Introduction to Graduate Mathematics
4:00 pm   in 245 Altgeld Hall,  Wednesday, March 14, 2012
 Del Edit Copy
Submitted by seminar.
 Maarten Bergvelt (Department of Mathematics, University of Illinois at Urbana-Champaign)Integrable Systems and Cluster AlgebrasAbstract: Integrable system occur in many areas of mathematics (and physics). I will give an overview, ending with a brief discussion of the (still obscure) relation with cluster algebras.

Wednesday, April 11, 2012

Math 499: Introduction to Graduate Mathematics
4:00 pm   in 245 Altgeld Hall,  Wednesday, April 11, 2012
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Submitted by seminar.
 Zoi Rapti (Department of Mathematics, University of Illinois at Urbana-Champaign)DNA modeling and Klein-Gordon chainsAbstract: We will start with an overview of how we can model DNA taking into account only the major interactions between the nucleobases. This is coarse-grained enough that will later allow us to use Klein-Gordon equations to describe the DNA dynamics. In particular, we will focus on time-periodic spatially localized solutions and we will use Floquet theory to analyze their linear stability.

Wednesday, April 18, 2012

Math 499: Introduction to Graduate Mathematics
4:00 pm   in 245 Altgeld Hall,  Wednesday, April 18, 2012
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Submitted by seminar.
 Zhong-Jin Ruan (Department of Mathematics, University of Illinois at Urbana-Champaign)Operator Algebras--Noncommutative Topological/Measure Spaces

Wednesday, April 25, 2012

Math 499: Introduction to Graduate Mathematics
4:00 pm   in 245 Altgeld Hall,  Wednesday, April 25, 2012
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Submitted by seminar.
 Aimo Hinkkanen (Department of Mathematics, University of Illinois at Urbana-Champaign)Complex analysis of one variable

Wednesday, May 2, 2012

Math 499: Introduction to Graduate Mathematics
4:00 pm   in 245 Altgeld Hall,  Wednesday, May 2, 2012
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Submitted by seminar.
 Vadim Zharnitsky (Department of Mathematics, University of Illinois at Urbana-Champaign)Hamiltonian dynamics and billiard systems

Wednesday, August 29, 2012

Math 499: Introduction to Graduate Mathematics
4:00 pm   in 245 Altgeld Hall,  Wednesday, August 29, 2012
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Submitted by laugesen.
 Richard Laugesen   [email] (UIUC Math)Eigenvalues of the LaplacianAbstract: The fundamental processes of classical physics are diffusion and wave motion. Quantum mechanics too is a kind of wave phenomenon. Mathematically, these processes can all be decomposed in terms of eigenfunctions (states) and eigenvalues (frequencies) of the Laplacian (the sum of pure second partial derivatives). What do we know about those eigenvalues? What would we like to know? I will concentrate on isoperimetric problems that stretch back to Queen Dido in antiquity and Lord Rayleigh in the 19th century, and continue into the future.

Wednesday, September 5, 2012

Math 499: Introduction to Graduate Mathematics
4:00 pm   in 245 Altgeld Hall,  Wednesday, September 5, 2012
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Submitted by laugesen.
 Philipp Hieronymi   [email] (UIUC Math)An invitation to Mathematical LogicAbstract: I will give a short introduction to Mathematical Logic and the research carried out by members of the Logic group here in Urbana. I will present some of the fundamental theorems of Mathematical Logic established in first part of the 20th century, and then compare these to the research done today.

Wednesday, September 12, 2012

Math 499: Introduction to Graduate Mathematics
4:00 pm   in 245 Altgeld Hall,  Wednesday, September 12, 2012
 Del Edit Copy
Submitted by laugesen.
 John D'Angelo   [email] (Department of Mathematics, University of Illinois at Urbana-Champaign)Inequalities from Complex AnalysisAbstract: After a short discussion about complex analysis in one and several variables, I discuss two specific interesting inequalities about integrals. In each case I give two proofs (in the one variable setting) to help glimpse deeper waters.

Wednesday, September 19, 2012

Math 499: Introduction to Graduate Mathematics
4:00 pm   in 245 Altgeld Hall,  Wednesday, September 19, 2012
 Del Edit Copy
Submitted by laugesen.
 Alexandr Kostochka   [email] (UIUC Math)On k-color-critical n-vertex graphs with fewest edgesAbstract: A graph $G$ is $k$-{\em critical} if it has chromatic number $k$, but every proper subgraph of $G$ is $(k-1)$--colorable. Let $f_k(n)$ denote the minimum number of edges in an $n$-vertex $k$-critical graph. We give a lower bound, $f_k(n) \geq F(k,n)$, that is sharp for every $n=1\,({\rm mod }\,$ It is also sharp for $k=4$ and every $n\geq 6$. The result improves the classical bounds by Gallai and Dirac and some subsequent bounds. It establishes the asymptotics of $f_k(n)$ for every fixed $k$. It also proves that the conjecture by Ore from 1967 that for every $k\geq 4$ and $n\geq k+2$, $f_k(n+k-1)=f(n)+\frac{k-1}{2}(k - \frac{2}{k-1})$ holds for each $k\geq 4$ for all but at most $k^3/12$ values of $n$. The result has interesting applications. One of the corollaries of the theorem is a half-page proof of the theorem due to Gr\" otzsch that every triangle-free planar graph is $3$-colorable.

Wednesday, September 26, 2012

Math 499: Introduction to Graduate Mathematics
4:00 pm   in 245 Altgeld Hall,  Wednesday, September 26, 2012
 Del Edit Copy
Submitted by laugesen.
 Ely Kerman   [email] (Department of Mathematics, University of Illinois at Urbana-Champaign)Hamiltonian dynamical systems and their periodic orbits Abstract: In this talk I will introduce the notion of a Hamiltonian dynamical system and discuss several theorems and open problems concerning their periodic orbits. We will start with basic examples from classical mechanics and a beautiful theorem of Henri Poincare, and will work our way up to problems at the forefront of current research activity.

Wednesday, October 3, 2012

Math 499: Introduction to Graduate Mathematics
4:00 pm   in 245 Altgeld Hall,  Wednesday, October 3, 2012
 Del Edit Copy
Submitted by laugesen.
 Florin Boca   [email] (UIUC Math)Angular distribution of lattices points and related geometric probability problemsAbstract: We will discuss some problems arising from the study of various discrete periodic configurations of points in Euclidean or Hyperbolic spaces. The associated distribution of angles is of particular interest to us. Ideas and methods from Number Theory, Ergodic Theory and Dynamical Systems that play an important role in the study of this kind of problems will be outlined.

Wednesday, October 10, 2012

Math 499: Introduction to Graduate Mathematics
4:00 pm   in 245 Altgeld Hall,  Wednesday, October 10, 2012
 Del Edit Copy
Submitted by laugesen.
 Rui Fernandes (Department of Mathematics, University of Illinois at Urbana-Champaign)What is Poisson geometry?Abstract: Poisson Geometry is an amalgam of three classical theories: (it is) Foliation Theory (inside which) Symplectic Geometry and Lie Theory (interact with each other). In this talk I will explain how Poisson geometry grew out of classical mechanics and discuss some of its modern developments and open problems.

Wednesday, October 24, 2012

Math 499: Introduction to Graduate Mathematics
4:00 pm   in 245 Altgeld Hall,  Wednesday, October 24, 2012
 Del Edit Copy
Submitted by laugesen.
 Ilya Kapovich   [email] (UIUC Math)Groups as geometric objectsAbstract: Geometric group theory is a vibrant and rapidly developing area of mathematics that lies at the juncture of group theory, low-dimensional topology, differential geometry and several other subjects. A crucial idea in the area is to view a finitely generated group as a geometric and not just as an algebraic object. One of the key tools for realizing this goal is the notion of the Cayley graph of a group, which is a metric space associated to a finitely generated group together with a finite generating set. Geometric group theory studies the connections between large-scale geometric properties of groups on one side and their algebraic and algorithmic properties on the other side. In this introductory talk we will explore the basic ideas and notions of the subject and demonstrate how the above connections manifest themselves in a number of representative results.

Wednesday, October 31, 2012

Math 499: Introduction to Graduate Mathematics
4:00 pm   in 245 Altgeld Hall,  Wednesday, October 31, 2012
 Del Edit Copy
Submitted by laugesen.
 Sergiy Merenkov   [email] (Department of Mathematics, University of Illinois at Urbana-Champaign)Rigidity in complex analysis and its discrete counterpartsAbstract: I will start by recalling several rigidity (uniqueness) phenomena in classical complex analysis, then draw parallels with similar questions for circle packings, and finally discuss analogous statements in quasiconformal geometry of carpets and related sets.

Wednesday, November 7, 2012

Math 499: Introduction to Graduate Mathematics
4:00 pm   in 245 Altgeld Hall,  Wednesday, November 7, 2012
 Del Edit Copy
Submitted by laugesen.
 Kay Kirkpatrick (UIUC Math)A random walk through statistical mechanics: scaling limits and supercool phenomenaAbstract: One of the main goals in statistical mechanics is to derive a macroscopic description of matter from the microscopic interacting particles via scaling limits. I will discuss recent advances on a supercooled phase of matter called Bose-Einstein condensation, in which a gas of quantum particles condenses and behaves like a giant quantum particle. I'll also discuss some challenges for understanding superconductors mathematically, and I'll mention related work in progress.

Wednesday, November 14, 2012

Math 499: Introduction to Graduate Mathematics
4:00 pm   in 245 Altgeld Hall,  Wednesday, November 14, 2012
 Del Edit Copy
Submitted by laugesen.
 Renming Song   [email] (UIUC Math)An Introduction to Subordinate Brownian MotionsAbstract: A Levy process is a process with stationary and indpendent increments. Levy processes have been widely used in various fields. However, the class of Levy processes is very large and not very tractable. A subordinate Brownian motion is a Levy process that can be obtained by replacing the time parameter of a Brownian motion by an increasing Levy process (i.e.,subordinator). The subordinator can be thought of as the "operational time" or "intrinsic time". Subordinate Brownian motions form a large sublclass of Levy processes and yet they much more tractable than general Levy processes. In this talk, I will give a brief introduction to subordinate Brownian motions.

Wednesday, November 28, 2012

Math 499: Introduction to Graduate Mathematics
4:00 pm   in 245 Altgeld Hall,  Wednesday, November 28, 2012
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Submitted by laugesen.
 Abstract: Instead of the usual Math 499 today, we will attend the Trjitzinsky Memorial Lecture. It will help to have attended yesterday's lecture also.

Wednesday, December 5, 2012

Math 499: Introduction to Graduate Mathematics
4:00 pm   in 245 Altgeld Hall,  Wednesday, December 5, 2012
 Del Edit Copy
Submitted by laugesen.
 Burak Erdogan   [email] (UIUC Math)Summability problems in Fourier analysis with applications to geometric measure theory and PDEs

Wednesday, December 12, 2012

Math 499: Introduction to Graduate Mathematics
4:00 pm   in Altgeld Hall,  Wednesday, December 12, 2012
 Del Edit Copy
Submitted by laugesen.
 No meeting this weekAbstract: Good luck with exams!