July 16th-July 26th, 2018

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

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 |

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

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

Problem Set 1

Problem Set 2

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

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

Problem Set 1

Problem Set 2

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

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