2nd Northwestern Summer School in Probability

SNAP 2018

Northwestern University
July 16th-July 26th, 2018

All lectures to be held in Lunt 105. Click here for a campus map.

Registration and coffee starts at 8.30am on Monday, July 16th.


Monday, July 16 Tuesday, July 17 Wednesday, July 18 Thursday, July 19 Friday, July 20 Saturday, July 21
9.00am - 10.30am Lalley Lalley Quastel Quastel Quastel Gorin
11.00am - 12.00pm Problem Session (Lalley) Problem Session (Lalley) Lalley Problem Session (Quastel) Problem Session (Quastel) Lalley
2.00pm - 3.30pm Gorin Gorin Free afternoon Gorin Lalley Free afternoon
4.00pm - 5.00pm Steve Zelditch (Special lecture) Problem Session (Gorin) Free afternoon Problem Session (Gorin) Problem Session (Lalley) Free afternoon

Monday July 16, 5.15pm there will be Pizza in the Mathematics Department Common Room, 2nd floor Lunt Hall


Monday, July 23 Tuesday, July 24 Wednesday, July 25 Thursday, July 26
9.00am - 10.30am Kosygina/Matic Kosygina/Matic Kosygina/Matic Kosygina/Matic
11.00am - 12.00pm Bakhtin Problem Session (Bakthin) Problem Session (Kosygina) Bakhtin
2.00pm - 3.30pm Bakhtin Bakhtin Bakhtin Free afternoon
4.00pm - 5.00pm Problem Session (Kosygina) Problem Session (Kosygina) Problem Session (Bakthin) Free afternoon

Titles and Abstracts:

Yuri Bakhtin   (Courant Institute). Title: Ergodic theory of the stochastic Burgers equation

Lecture Notes

Problem set

This course will be based on the following research papers:

Space-time stationary solutions for the Burgers equation

Inviscid Burgers equation with random kick forcing in noncompact setting

Thermodynamic limit for directed polymers and stationary solutions of the Burgers equation

Zero temperature limit for directed polymers and inviscid limit for stationary solutions of stochastic Burgers equation

Vadim Gorin   (MIT). Title: Tilings, matrices, and representations through Schur generating functions

Lecture notes

Problem Set 1

Problem Set 2

Elena Kosygina and Ivan Matic   (CUNY - Baruch College). Title: Large deviations through examples.

Syllabus (The books cited here are available for easy access at the Math library).

Lecture 1

Lecture 2

Lecture 3

Lecture 4

Problem Set 1

Problem Set 2

Problem Set 3

Steve Lalley   (University of Chicago). Title: Random Walks on Infinite Discrete Groups

Lecture notes

Problem Set 1

Problem Set 2

Jeremy Quastel   (Toronto). Title: TASEP and the KPZ fixed point

Lecture notes

Special Lecture: Steve Zelditch (Northwestern) Title: Complex zeros of random polynomials.

Abstract: A random polynomial is a polynomial $p_N(z) = \sum_{k=0}^N a_k z^k$ of one complex variable whose coefficients $a_k$ are random variables. Mark Kac introduced the simplest Gaussian random polynomial in the 50's, where the $a_k$ are i.i.d. N(0,1). Kac and Hammersley studied the zeros of $p_N(z)$ and found that the complex zeros cluster around the unit circle. My talk is devoted to the question: what in the Kac-Hammersley definition of of $a_k$ caused this strange distribution of zeros? Could we have designed the random variables $a_k$ to get any distribution of zeros?

Lecture Notes