JOINT DEPARTMENT OF MATHEMATICS AND CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX AND PROBABILITY THEORY SEMINAR: | Alexander FriberghUniversité de Montréal |
The ant in the labyrinth |

on Wednesday, March 22, 2017, at 3:00 PM in CMSA Building, 20 Garden St, G10 | ||

One of the most famous open problem in random walks in random environments is to understand the behavior of a simple random walk on a critical percolation cluster, a model known as the ant in the labyrinth. I will present new results on the scaling limit for the simple random walk on the critical branching random walk in high dimension. In the light of lace expansion, we believe that the limiting behavior of this model should be universal for simple random walks on critical structures in high dimensions. |

NUMBER THEORY SEMINAR: | Peter SarnakPrinceton University |
Integral points on Markoff type cubic surfaces |

on Wednesday, March 22, 2017, at 3:00 pm in Science Center 507 | ||

Cubic surfaces in affine three space tend to have few integral points. Certain cubics such as x^3+y^3+z^3=m , may have many such points but very little is known about them. After a brief review of these questions we focus on Markoff type surfaces : x^2+y^2+z^2-x.y.z= m , for which a (nonlinear) descent is a starting point to investigate a Hasse Principle and strong approximation. Joint works with Ghosh and Bourgain/Gamburd. |

INFORMAL GEOMETRY & DYNAMICS SEMINAR: | Oleg IvriiCalifornia Institute of Technology |
Differentiating Blaschke products |

on Wednesday, March 22, 2017, at 4:00 pm in Science Center 507 |

THURSDAY SEMINAR : | Jacob LurieHarvard University |
Etale motivic cohomology |

on Thursday, March 23, 2017, at 3:00 - 5:00 PM in Science Center 507 |

JOINT DEPARTMENT OF MATHEMATICS AND CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX AND PROBABILITY THEORY SEMINAR: | Nina HoldenMIT |
Percolation-decorated triangulations and their relation with SLE and LQG |

on Wednesday, March 29, 2017, at 3:00 pm in CMSA Building, 20 Garden St, G02 | ||

The Schramm-Loewner evolution (SLE) is a family of random fractal curves, which is the proven or conjectured scaling limit of a variety of two-dimensional lattice models in statistical mechanics, e.g. percolation. Liouville quantum gravity (LQG) is a model for a random surface which is the proven or conjectured scaling limit of discrete surfaces known as random planar maps (RPM). We prove that a percolation-decorated RPM converges in law to SLE-decorated LQG in a certain topology. This is joint work with Bernardi and Sun. We then discuss a work in progress where we try to strengthen the topology of convergence of a RPM to LQG by considering conformal embeddings of the RPM into the complex plane. This is joint work with Sun and with Gwynne, Miller, Sheffield, and Sun. |

CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM: | Leslie GreengardCourant Institute |
Inverse problems in acoustic scattering and cryo-electron microscopy |

on Wednesday, March 29, 2017, at 4:00 pm in CMSA Building, 20 Garden St, G10 | ||

A variety of problems in image reconstruction give rise to large-scale, nonlinear and non-convex optimization problems. We will show how recursive linearization combined with suitable fast solvers are bringing such problems within practical reach, with an emphasis on acoustic scattering and protein structure determination via cryo-electron microscopy. |

DIFFERENTIAL GEOMETRY SEMINAR: | Chiu-Chu Melissa LiuColumbia University |
GW theory, FJRW theory, and MSP fields |

on Tuesday, April 04, 2017, at 2:45 pm in CMSA Building, 20 Garden St, G10 | ||

Gromov-Witten (GW) invariants of the quintic Calabi-Yau 3-fold are virtual counts of parametrized holomorphic curves to the quintic 3-fold. Fan-Jarvis-Ruan-Witten (FJRW) invariants of the Fermat quintic polynomial are virtual counts of solutions to the Witten equation associated to the Fermat quintic polynomial. In this talk, I will describe the theory of Mixed-Spin-P (MSP) fields interpolating GW theory of the quintic 3-fold and FJRW theory of the Fermat quintic polynomial, based on joint work with Huai-Liang Chang, Jun Li, and Wei-Ping Li. |

JOINT DEPARTMENT OF MATHEMATICS AND CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX AND PROBABILITY THEORY SEMINAR: | Steven HellmanUCLA |
Noncommutative Majorization Principles and Grothendieck's Inequality |

on Wednesday, April 05, 2017, at 3:00 pm in CMSA Building, 20 Garden St, G10 | ||

The seminal invariance principle of Mossel-O'Donnell-Oleszkiewicz implies the following. Suppose we have a multilinear polynomial Q, all of whose partial derivatives are small. Then the distribution of Q on i.i.d. uniform {-1,1} inputs is close to the distribution of Q on i.i.d. standard Gaussian inputs. The case that Q is a linear function recovers the Berry-Esseen Central Limit Theorem. In this way, the invariance principle is a nonlinear version of the Central Limit Theorem. We prove the following version of one of the two inequalities of the invariance principle, which we call a majorization principle. Suppose we have a multilinear polynomial Q with matrix coefficients, all of whose partial derivatives are small. Then, for any even K>1, the Kth moment of Q on i.i.d. uniform {-1,1} inputs is larger than the Kth moment of Q on (carefully chosen) random matrix inputs, minus a small number. The exact statement must be phrased carefully in order to avoid being false. Time permitting, we discuss applications of this result to anti-concentration, and to computational hardness for the noncommutative Grothendieck inequality. (joint with Thomas Vidick) https://arxiv.org/abs/1603.05620 |

Subhajit GoswamiUniversity of Chicago |
Liouville first-passage percolation and Watabiki's prediction | |

on Wednesday, April 12, 2017, at 3:00 pm in CMSA Building, 20 Garden St, G10 | ||

In this talk I will give a brief introduction to Liouville first-passage percolation (LFPP) which is a model of random metric on a finite planar grid graph. It was studied primarily as a way to make sense of the random metric associated with Liouville quantum gravity (LQG), one of the major open problems in contemporary probability theory. I will discuss some recent results on this metric and the main focus will be on estimates of the typical distance between two points. I will also discuss about the apparent disagreement of these estimates with a prediction made in the physics literature about LQG metric. The talk is based on a joint work with Jian Ding. |

SPECIAL BASIC NOTIONS SEMINAR: | Jean-Pierre SerreCollège de France |
Some simple facts on lattices and orthogonal group representations |

on Wednesday, May 03, 2017, at 3:00 pm in Science Center Hall D | ||

Afternoon tea will follow at 4:15 pm in the Math Department Common Room, 4th floor. |

SPECIAL LECTURE SERIES: | Jean-Pierre SerreCollège de France |
Cohomological invariants mod 2 of Weyl groups, Pt. 1 |

on Monday, May 08, 2017, at 3:00 - 4:00 PM in Science Center 507 | ||

The first lecture will mostly be a résumé of the first part of AMS ULECT 28; the second lecture will give an explicit description of the cohomological invariants of the Weyl groups. *Afternoon tea will follow the talks at 4:15 pm in the Math Department Common Room, 4th Floor. |

SPECIAL LECTURE SERIES: | Jean-Pierre SerreCollège de France |
Cohomological invariants mod 2 of Weyl groups, Pt. 2 |

on Tuesday, May 09, 2017, at 3:00 - 4:00 PM in Science Center 507 | ||

The first lecture will mostly be a résumé of the first part of AMS ULECT 28; the second lecture will give an explicit description of the cohomological invariants of the Weyl groups. *Afternoon tea will follow the talks at 4:15 pm in the Math Department Common Room, 4th Floor. |