Weekly Calendar

March 19-23, 2001

Monday Tuesday Wednesday Thursday Friday

Seminars Announcements Conferences Calendar Archive

Items for inclusion in the Weekly Calendar should be submitted via e-mail to Hilda Britt. Deadline for inclusion in the Weekly Calendar is 5 p.m. Thursdays. Speakers are encouraged to provide abstracts.

Orange & Blue Bar

MONDAY, MARCH 19

3269 Beckman institute, 3:00 p.m.
THEORETICAL BIOPHYSICS SEMINAR
Dr. Ivo Hofacker, Institut fuer Theoretische Chemie, Wien, Austria
RNA Energy Landscapes and Folding Kinetics
Abstract: The ability to fold into a well-defined native conformation is a prerequisite for biological functional biopolymers. In the case of RNA, secondary structures provide a computationally feasible model, in which most thermodynamic quantities of interest such as the ground state and partition function can be computed efficiently via dynamic programming. Such equilibrium properties are, however, not sufficient to characterize the folding behavior. To investigate the folding dynamics of an RNA sequence, we consider the energy landscape formed by all possible conformations (secondary structures). By enumerating all conformations within a predefined energy range, we obtain a detailed picture of the energy landscape in the vicinity of the ground state. In particular we are able to identify local minima, as well as measure their basins of attraction and the energy barriers separating them. This analysis of the landscape can be compared to detailed folding simulations using a Monte Carlo technique, as well as experimental data on some biologically relevant sequences. Folding kinetics depend strongly on the highest energy barrier present in the landscape, and barriers high enough to stabilize mis-folded states over biologically relevant times, can occur even for relatively short sequences. Such sequences can be design easily and may serve as molecular switches. Typical sequences exhibit a small number of significant local minima, which can be reached quickly from the unfolded state. For moderate length sequences the energy barriers between these local minima usually allow re-folding to the ground state.

Tea and coffee will be served in R3151 Beckman Institute at 2:15pm.

245 Altgeld Hall, 4:00 p.m.
MATH 400 - INTRODUCTION TO GRADUATE MATHEMATICS
Professor Ken Stolarsky, Department of Mathematics, UIUC
Polynomials in One Complex Variable

TUESDAY, MARCH 20

345 Altgeld Hall, 11:00 a.m.
MAX NEW TOPOLOGY
No meeting this week

2 Illini Hall, 11:00 a.m.
PROBABILITY AND STATISTICS SEMINAR
TBA

243 Altgeld Hall, 12:00 p.m.
SEVERAL COMPLEX VARIABLES SEMINAR
No meeting this week

241 Altgeld Hall, 1:00 p.m.
ANALYTIC NUMBER THEORY
10 minute talks

243 Altgeld Hall, 1:00 p.m.
LOGIC SEMINAR
Professor Wai Yan Pong, Department of Mathematics, UIUC
A Well Ordering on Kolchin Polynomials
Abstract: Sit showed that the Kolchin Polynomials (in the Char 0 case) are well ordered by the dominance ordering of polynomials. I will give a short proof of this result and discuss the Char p > 0 case.

243 Altgeld Hall, 2:00 p.m.
NONSTANDARD ANALYSIS
Professor Yevgeniy Gordon, Visitor, Nizhnii Novgorod State University
Kachurivskii's proof of ergodic theorem based on nonstandard analysis
Abstract: We continue to discuss the Thesis of Kachurivskii, where a new proof of ergodic theorem based on Rokhlin-Halmos Lemma and nonstandard analysis was introduced.

345 Altgeld Hall, 2:00 p.m.
SPACES OF NON-POSITIVE CURVATURE RAP
Craig Davis, UIUC
Convexity of the metric and rigidity of flat shapes in CAT(0)-spaces
Abstract:We will discuss the convexity of the distance function on CAT(0)-spaces and geometric centers of bounded sets.

We will also show that a geodesic triangle in a CAT(0)-space, which is ``no thinner" than the corresponding comparison triangle, is itself Euclidean or ``flat".

241 Altgeld Hall, 2:00 p.m.
STOCHASTIC AND NONLINEAR ANALYSIS
TBA

159 Altgeld Hall, 3:00 p.m.
COMMUTATIVE RING THEORY RAP
Professor Sean Sather-Wagstaff, Department of Mathematics, UIUC
Intersections of Symbolic Powers of Prime Ideals in Regular Local Rings

241 Altgeld Hall, 3:00 p.m.
GEOMETRIC POTPOURRI SEMINAR
Professor Vincent J. Matsko, Quincy University
Permutahedra Relative to a Regular Polytope
Abstract: The classical permutahedron is usually described as the convex hull of the images of a point under the symmetry group of an n-dimensional simplex. This idea may be generalized by examining the convex hull of the images of a point under the symmetry group of a given regular polytope.

345 Altgeld Hall, 3:00 p.m.
GRAPH THEORY AND COMBINATORICS
Professor Yoshiyasu Ishigami
An Extension of a Theorem of Alon and Yuster in Extremal Graph Theory
Abstract:Alon and Yuster [1992] proved the following theorem about packing of graphs. Let H be a fixed r-chromatic graph, and let G be a graph of order n. Their theorem asserts that if n is sufficiently large and G has minimumdegree at least (1-1/r)n, then G contains vertex-disjoint copies of H covering almost all vertices of G (all but en). When H = Kr, the theorem gives an asymptotic version of the Hajnal-Szemeredi Theorem [1970].

We improve the theorem by showing that the conclusion still holds whenever H has order at most clogn, where c is independent of n (it depends on r and e). This magnitude of |H| is best possible. Our proof method is quite different from the original proof of 1992. We will also present related results, including a common extension of the Erdos-Stone Theorem and the Alon-Yuster Theorem.

Note: Prof. Ishigami has been visiting this campus for almost two years. He will leave to return to Japan at the end of this month.

WEDNESDAY, MARCH 21

243 Altgeld Hall, 4:00 p.m.
VERTEX ALGEBRA AND ELLIPTIC GENUS
Panagiotis Panagopoulos
Introduction to gerbes II

114 CSRL, 4:30 p.m.
INFORMATION PROTECTION SEMINAR
Dr. Edlyn Teske, University of Waterloo
Computing discrete logarithms with rho and kangaroo methods
Abstract: The security of several important public-key cryptographic systems is based on the difficulty of the discrete logarithm problem. In arbitrary cyclic groups, the most powerful methods known to date to compute discrete logarithms are the parallel Pollard rho and kangaroo methods. In particular, the methods apply to the elliptic curve discrete logarithm problem, thereby stimulating substantial interest in these methods from cryptographers.

In our talk, we discuss algorithmic and computational aspects of both methods, recent developments, and cryptographic implications.

THURSDAY, MARCH 22

ESB 6.110, 12:00 p.m.
MATH - PHYSICS (BCDE) LUNCH SEMINAR
Mr. Vishnu Jejjala, Department of Physics, UIUC
D-branes and boundary states

241 Altgeld Hall, 1:00 p.m.
ANALYTIC NUMBER THEORY
Professor Bruce Berndt, Department of Mathematics, UIUC
Proof of an incorrect formula in Ramanujan's lost notebook

347 Altgeld Hall, 1:00 p.m.
GROUP THEORY SEMINAR
Peter Brinkmann, Department of Mathematics, UIUC
Diagram groups
Abstract: I will introduce the notion of diagram groups according to Sapir and Guba. The aim is to show that diagram groups are CAT(0) (this is a recent result due to D. Farley) and that Thompson's group F is a diagram group (this is one of the fundamental results in this area, due to Guba).

241 Altgeld Hall, 2:00 p.m.
ALGEBRAIC GROUPS AND THEIR REPRESENTATIONS
Frobenius Splitting of Sehubert Cells

243 Altgeld Hall, 2:00 p.m.
ALGEBRAIC NUMBER THEORY
Professor Michael Bennett, Department of Mathematics, UIUC
Cannonballs and Congruent Numbers

347 Altgeld Hall, 2:00 p.m.
ANALYSIS SEMINAR
TBA

145 Altgeld Hall, 3:00 p.m.
COLORING THEORY RESEARCH GROUP
Discussion of open problems

243 Altgeld Hall, 3:00 p.m.
COMMUTATIVE RING THEORY RAP
Professor Phillip Griffith, Department of Mathematics, UIUC
Projective Schemes, continued

141 CSRL, 3:00 p.m.
DECISION, CONTROL AND OPTIMIZATION SEMINAR
Professor Bruce Reznick, Department of Mathematics, UIUC
How to write a polynomial as a sum of squares of polynomials, and why you'd want to do so
Abstract: One of the fundamental questions one can ask about a real polynomial is whether it only takes non-negative values; such a polynomial is called psd. Both pure and applied mathematicians frequently wish to know whether a particular polynomial is psd. If a polynomial can be written as a sum of squares of polynomials - such a polynomial is called sos - then it is evidently psd. For polynomials in one variable or quadratic forms, these two conditions coincide, but in 1888, David Hilbert showed that there exist more complicated psd polynomials in more variables and higher degree which are not sos. The 17th of Hilbert's famous list of 23 problems asked the variant question of whether every psd polynomial is a sum of squares of rational functions. Artin answered affirmatively in the 1920s, though with an abstract proof that gives no hint of how one might find such a representation. And Hilbert's original example was cast in the difficult language of 19th century curve theory, and did not attract much interest until the mid 60s. In the mid-60s, Theodore S. Motzkin and Raphael M. Robinson independently found separate simplifications of Hilbert's example, which then brought new light onto the subject. Their examples are:
M(x,y) = x4y2 +x2y4 + 1 - 3x2y2,
R(x1,x2,x3) = 3
Â
 i = 1 
 xi6 -
Â
 i ¼ j 
 xi4xj2 + 3x12x22x32.
The proofs that these are psd and not sos come from ``The Book", in the sense of Erdös. This talk will discuss the work of M.D. Choi, T.Y. Lam, Pablo Parrilo, the speaker and others, done over the last 25 years. We now know an effective algorithm for determining whether a given psd polynomial is sos. We also have an explicit formula for writing a psd polynomial without zeros as a sum of squares of rational functions. The talk will be expository, go lightly on abstraction and present many concrete examples.

NOTE: Coffee and cookies at 2:40pm before the seminar in Room 154 C&SRL.

347 Altgeld Hall, 3:00 p.m.
GALOIS MODULES
TBA

245 Altgeld Hall, 4:00 p.m.
MATHEMATICS COLLOQUIUM
Bruce P. Palka, Department of Mathematics, University of Texas, Austin
Why things go quasi in higher dimensions!
Abstract: This talk will discuss Liouville's 1850 theorem to the effect that there is a general paucity of conformal mappings in Euclidean spaces of dimension three and above - say, in comparison with the situation in the plane, where the Riemann mapping theorem ensures a wealth of conformal mappings. The talk should be accessible to graduate students, and even to advanced undergraduates.

Refreshments at 3:15 pm in Room 321 Altgeld Hall

FRIDAY, MARCH 23

243 Altgeld Hall, 4:00 p.m.
MODEL THEORY SEMINAR
Mr. James Tyne UIUC
Expansions of algebraically closed fields in o-minimal structures
Abstract:We continue to study the paper of Peterzil and Starchenko with the same title.