# Week of 14 September 2014 Mathematics Seminars

## Colloquia

### Regularity properties of solutions to the hysteresis-type problem

##### Nina Uraltseva (Saint Petersburg State University)
Abstract: The heat equation with the simplest hysteresis operator on the right-hand side will be considered. Such equations describe the so-called processes "with memory" in which various substances interact according to the hysteresis law. Various definitions of solutions will be discussed. The most attention will be paid to the so-called "strong solutions" belonging to the Sobolev class $W^{2,1}_q$ with sufficiently large $q$. For such solutions the optimal regularity, $q=\infty$, is proved outside some "pathological" part of the free boundary. The arguments are based on quadratic growth estimates for solutions near the free boundary.

### Erdo"s Magic

##### Joel Spencer (Courant Institute, NYU)
Abstract: The twentieth century saw the elevation of Discrete Mathematics from "the slums of topology" (one of the more polite expressions!) to its current highly regarded position in the mathematical pantheon. Paul Erdo"s played a key role in this transformation. We call discuss some key results, possibly including: ( i ) Ramsey Theory. In 1946 Erdo"s showed that you could two-color the complete graph on n vertices so as to avoid a monochromatic clique of size k, where n was exponential in k. To do it, he introduced The Probabilistic Method. ( ii ) Two-Coloring. In 1963 Erdo"s showed that given any m<2^{n-1} sets, each of size n, one could two-color the underlying points so that none of the sets were monochromatic. His proof in two words: Color Randomly! There has been much work on larger m. We give a simple algorithm (together with a subtle analysis) of Cherkashin and Kozik that finds a coloring for the best known (so far!) m. ( iii ) Number Theory. In 1940 Erdo"s, with Marc Kac, showed that the number of prime factors of n satisfies (when appropriately defined) a Gaussian distribution. Amazing! ( iv ) Liar Games. Paul tries to find an integer ...

### Monday, 15 September 2014

#### Topology Seminar

To be announced at 2:30p.m. in VinH 570

#### Automorphic Forms and Number Theory

Local and global automorphic Sobolev spaces, application to meromorphic continuations at 3:35p.m. in 206 Vincent Hall
Paul Garrett

### Tuesday, 16 September 2014

#### Colloquium

Regularity properties of solutions to the hysteresis-type problem at 3:30p.m. in Vin H 16
Nina Uraltseva (Saint Petersburg State University)
The heat equation with the simplest hysteresis operator on the right-hand side will be considered. Such equations describe the so-called processes "with memory" in which ... (more)

### Wednesday, 17 September 2014

#### Math Physics Seminar

An introduction to moving frames at 12:20p.m. in VinH 570
Professor Peter Olver (U of M Mathematics Department)

#### Algebraic Geometry

Preparation for Kisin's lectures: p-curvature and the Grothendieck-Katz Conjecture II at 2:30p.m. in VinH 313
William Messing (U of M)

#### Reading Seminar on Automorphic Forms

To be determined at 3:30p.m. in VinH 209
Professor Dihua Jiang (U of M Mathematics Department)
To be announced

### Thursday, 18 September 2014

#### Commutative Algebra Seminar

Cellular binomial ideals at 11:15a.m. in VinH 203A
Laura Felicia Matusevich
A binomial ideal I is cellular if every variable is either nilpotent or a nonzerodivisor modulo I. Since any binomial ideal has an effectively computable ... (more)

#### Math Club Seminar

The Mathematician and the Devil at 12:20p.m. in VinH 570
TBA.

#### Colloquium

Erdo"s Magic at 3:30p.m. in VinH 16
Joel Spencer (Courant Institute, NYU)
The twentieth century saw the elevation of Discrete Mathematics from "the slums of topology" (one of the more polite expressions!) to its current highly regarded ... (more)

### Friday, 19 September 2014

#### IMA/MCIM Industrial Problems Seminar

Regularization in the Real World at 1:25p.m. in Lind 305
Eric Voth (St. Jude Medical)

#### Combinatorics Problem Session

All are welcome to pose a short combinatorics problem, or discuss problems posed by others at 2:30p.m. in VinH 570
to be announced

#### Probability Seminar

The diameter and longest paths in random Apollonian networks at 2:30p.m. in VinH 207
Professor Nick Wormald (Monash University)
Start with a triangle embedded in the plane. In each step, choose a bounded face uniformly at random, add a vertex inside that face and ... (more)

#### Lie Theory Seminar

Siegel Domains at 3:30p.m. in VinH 209
Professor Dihua Jiang (U of M Mathematics Department)
To be announced

#### Combinatorics Seminar

Combinatorics of clans and geometry of B-orbits on GL(n)/(GL(p) x GL(q)) at 3:35p.m. in VinH 570
Alexander Woo (University of Idaho)
Many aspects of the combinatorics of Weyl groups turn out to be useful in understanding the geometry of Schubert varieties (which are B-orbit closures) in ... (more)

#### MCFAM Seminar

Dr. Zizhuo Wang - A Unified Framework for Dynamic Prediction Market Design at 5:30p.m. in VinH 16
Dr. Zizhuo Wang (Department of Industrial Systems Engineering (ISyE), University of Minnesota)
Recently, coinciding with and perhaps driving the increased popularity of prediction markets, several novel pari-mutuel mechanisms have been developed such as the logarithmic market-scoring rule ... (more)

### Seminars Not Meeting This Week

Algebra Reading Seminar on Thursday at 2:00p.m. in VinH 2.
AMS Student Chapter seminar on Wednesday at 12:20p.m. in VinH 301.
Bobkov Student Seminar on Thursday at 1:15p.m. in Lind Hall 401.
Climate Seminar on Tuesday at 11:15a.m. in Vincent Hall 570.
Cockburn's Seminar on Friday at 2:30a.m. in VinH 364.
Combinatorics Study Group on Tuesday at 1:25p.m. in VinH 203A.
Differential Geometry / Symplectic Topology Seminar on Tuesday at 1:30p.m. in VinH 570.
Geometric Analysis Learning Seminar on Tuesday at 3:30p.m. in VinH 206.
Geometric Analysis Seminar on Tuesday at 3:30p.m. in VinH 570.
Graduate Student Seminar on Friday at 12:15p.m. in VinH 16.
IMA Postdoc Seminar on Tuesday at 1:20p.m. in Lind Hall 305.
IMA Public Lectures on Wednesday at 7:00p.m. in various locations.
Industrial Problems Seminar on Friday at 1:25a.m. in Lind Hall 305.
Introduction to Research on Friday at 12:20p.m. in VinH 2.
Jr. Colloquium on Wednesday at 12:20p.m. in VinH 16.
Math Biology Seminar on Wednesday at 2:30p.m. in VinH 364.
PDE Seminar on Wednesday at 3:35p.m. in VinH 206.
Postdoc Seminar on Thursday at 4:30p.m. in VinH 570.
SIAM Student reading group Seminar on Thursday at 11:00a.m. in VinH 570.
SIAM Student Seminar on Wednesday at 1:20a.m. in VinH 570.
Special Events and Seminars on Monday at 12:00p.m. in VinH.
Student Combinatorics Seminar on Tuesday at 1:30p.m. in FordH 155.
Student Number Theory Seminar on Tuesday at 1:15p.m. in VinH 570.
Student Stochastic Seminar on Wednesday at 3:00p.m. in VinH 364.
Student Symplectic and Low Dimensional Topology Seminar on Wednesday at 3:35a.m. in VinH 2.
Student Topology Seminar on Wednesday at 2:30p.m. in VinH 311.