JOINT DEPARTMENT OF MATHEMATICS AND CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX AND PROBABILITY THEORY SEMINAR: | Bob HoughStony Brook University |
Random walk on unipotent groups |

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

I will describe results of two recent papers from random walk on unipotent groups. In joint work with Diaconis (Stanford), we obtain a new local limit theorem on the real Heisenberg group, and determine the mixing time of coordinates for some random walks on finite unipotent groups. In joint work with Jerison and Levine (Cornell) we prove a cut-off phenomenon in sandpile dynamics on the torus $(\mathbb{Z}/m\mathbb{Z})^2$ and obtain a new upper bound on the critical exponent of sandpiles on $\mathbb{Z}^2$. |

NUMBER THEORY SEMINAR: | Yiwei SheIAS and Columbia University |
The (unpolarized) Shafarevich conjecture for K3 surfaces |

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

Let K be a number field, S a finite set of places of K, and g a positive integer. Shafarevich made the following conjecture for higher genus curves: the set of isomorphism classes of genus g curves defined over K and with good reduction outside of S is finite. Faltings proved this conjecture for curves and the analogous conjecture for polarized abelian surfaces and Zarhin removed the necessity of specifying a polarization. Building on the work of Faltings and Andre and using technical advances by Madapusi Pera, we prove the unpolarized Shafarevich conjecture for K3 surfaces. |

CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM: | Steven RayanUniversity of Saskatchewan |
Higgs bundles and the Hitchin system |

on Wednesday, February 22, 2017, at 4:30 pm in CMSA Building, 20 Garden St, G10 | ||

I will give an informal introduction to the Hitchin system, an object lying at the crossroads of geometry and physics. As a moduli space, the Hitchin system parametrizes semistable Higgs bundles on a Riemann surface up to equivalence. From this point of view, the Hitchin map and spectral curves emerge. We'll use these to form an impression of what the moduli space "looks like". I will also outline the appearances of the Hitchin system in dynamics, hyperkaehler geometry, and mirror symmetry. |

THURSDAY SEMINAR : | Mike HopkinsHarvard University |
Voevodsky's condition H90(n) |

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

HARVARD MIT ALGEBRAIC GEOMETRY SEMINAR: | Daniel LittColumbia University |
Arithmetic Restrictions on Geometric Monodromy |

on Tuesday, February 28, 2017, at 3:00 pm in MIT 4-153 | ||

Let X be an algebraic variety over a field k. Which representations of pi_1(X) arise from geometry, e.g. as monodromy representations on the cohomology of a family of varieties over X? We study this question by analyzing the action of the Galois group of k on the fundamental group of X. As a sample application of our techniques, we show that if X is a normal variety over a field of characteristic zero, and p is a prime, then there exists an integer N=N(X,p) satisfying the following: any irreducible, non-trivial p-adic representation of the fundamental group of X, which arises from geometry, is non-trivial mod p^N. |

DIFFERENTIAL GEOMETRY SEMINAR: | Nick EdelenMIT |
Quantitative Reifenberg for Measures |

on Tuesday, February 28, 2017, at 3:15 PM in CMSA Building, 20 Garden St, G10 | ||

In joint work with Aaron Naber and Daniele Valtorta, we demonstrate a quantitative structure theorem for measures in R^n under assumptions on the Jones \beta-numbers, which measure how close the support is to being contained in a subspace. Measures with this property have arisen in several interesting scenarios: in obtaining packing estimates on and rectifiability of the singular set of minimal surfaces; in characterizing L2-boundedness of Calderon-Zygmund operators; and as an “analyst’s” formulation of the traveling salesman problem. |

NUMBER THEORY SEMINAR: | David HansenColumbia University |
Some remarks on local Shimura varieties |

on Wednesday, March 01, 2017, at 3:00 pm in Science Center 507 | ||

I'll give an introduction to local Shimura varieties and (more generally) moduli spaces of mixed-characteristic local shtukas as defined by Scholze. I'll also discuss some recent results and conjectures on their geometry and cohomology. This is partially joint work with Jared Weinstein. |

CENTER OF MATHEMATICAL SCIENCES & APPLICATIONS COLLOQUIUM: | Jun LiuHarvard University Department of Statistics |
Expansion of biological pathways by integrative Genomics |

on Wednesday, March 01, 2017, at 4:30 PM in CMSA Building, 20 Garden St, G10 | ||

The number of publicly available gene expression datasets has been growing dramatically. Various methods had been proposed to predict gene co-expression by integrating the publicly available datasets. These methods assume that the genes in the query gene set are homogeneously correlated and consider no gene-specific correlation tendencies, no background intra-experimental correlations, and no quality variations of different experiments. We propose a two-step algorithm called CLIC (CLustering by Inferred Co-expression) based on a coherent Bayesian model to overcome these limitations. CLIC first employs a Bayesian partition model with feature selection to partition the gene set into disjoint co-expression modules (CEMs), simultaneously assigning posterior probability of selection to each dataset. In the second step, CLIC expands each CEM by scanning the whole reference genome for candidate genes that were not in the input gene set but co-expressed with the genes in this CEM. CLIC is capable of integrating over thousands of gene expression datasets to achieve much higher coexpression prediction accuracy compared to traditional co-expression methods. Application of CLIC to ~1000 annotated human pathways and ~6000 poorly characterized human genes reveals new components of some well-studied pathways and provides strong functional predictions for some poorly characterized genes. We validated the predicted association between protein C7orf55 and ATP synthase assembly using CRISPR knock-out assays. Based on the joint work with Yang Li and the Vamsi Mootha lab. |

JOINT DEPARTMENT OF MATHEMATICS AND CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX AND PROBABILITY THEORY SEMINAR: | 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. |