CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MATHEMATICAL PHYSICS SEMINAR : | Wenbin YanCMSA |
Argyres-Douglas Theories, Vertex Operator Algebras and Wild Hitchin Characters |

on Monday, February 27, 2017, at 12:00 PM in CMSA Building, 20 Garden St, G10 | ||

We discuss some interesting relations among 4d Argyles-Douglas (AD) theories, vertex operator algebras (VOA) and wild Hitchin system. We use the Coulomb branch index of AD theories to study geometric and topological data of moduli spaces of wild Hitchin system. These data show an one to one map between fixed points on the moduli space and irreducible modules of the VOA. Moreover, a limit of the Coulomb branch index of AD theories can be identified with matrix elements of the modular transform ST^kS in certain two-dimensional VOAs. The appearance of VOAs, which was known previously to be associated with Schur operators but not Coulomb branch operators, is somewhat surprising. |

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. |

JOINT DEPARTMENT OF MATHEMATICS AND CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX AND PROBABILITY THEORY SEMINAR: | Shirshendu GanglyUC Berkeley |
Large deviation and counting problems in sparse settings |

on Wednesday, March 01, 2017, at 3:00 PM in CMSA Building, 20 Garden St, G10 | ||

The upper tail problem in the Erd ̋os-R ́enyi random graph G ∼ Gn,p, where every edge is included independently with probability p, is to estimate the probability that the number of copies of a graph H in G exceeds its expectation by a factor 1 + δ. The arithmetic analog considers the count of arithmetic progressions in a random subset of Z/nZ, where every element is included independently with probability p. In this talk, I will describe some recent results regarding the solution of the upper tail problem in the sparse setting, i.e. where p decays to zero, as n grows to infinity. The solution relies on non-linear large deviation principles developed by Chatterjee and Dembo and more recently by Eldan and solutions to various extremal problems in additive combinatorics. |

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. |

INFORMAL GEOMETRY & DYNAMICS SEMINAR: | Russell LodgeStony Brook University |
Global dynamics of multi curves in complex dynamics |

on Wednesday, March 01, 2017, at 4:00 pm in Science Center 530 |

BRANDEIS, HARVARD, MIT, NORTHEASTERN JOINT MATHEMATICS COLLOQUIUM AT HARVARD: | Tony Yue YuUniversité Paris-Sud |
Counting open curves via Berkovich geometry |

on Thursday, March 02, 2017, at 4:30 PM in Science Center Hall A | ||

Motivated by mirror symmetry, we study the counting of open curves in log Calabi-Yau surfaces. Although we start with a complex surface, the counting is achieved by applying methods from Berkovich geometry (non-archimedean analytic geometry). This gives rise to new geometric invariants inaccessible by classical methods. These invariants satisfy a list of very nice properties and can be computed explicitly. If time permits, I will mention the conjectural wall-crossing formula, relations with the works of Gross-Hacking-Keel and applications towards mirror symmetry. |

HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR: | Bill FultonUniversity of Michigan |
Degeneracy Loci with a Line Bundle |

on Tuesday, March 07, 2017, at 3:00 pm in Science Center 507 | ||

In order to give formulas for classical as well as modern degeneracy loci, one needs to allow symplectic or quadratic forms on a vector bundle V with values in a line bundle L. If one has two flags of isotropic subbundles of V, one has a degeneracy locus for each signed permutation, specifying how they intersect. Finding formulas for their cohomology classes amounts to constructing double Schubert polynomials with a new parameter corresponding to the first Chern class of L. We construct these “twisted double Schubert polynomials” and show they satisfy all the analogues of the type A polynomials, including positivity for their coefficients and their products. This is joint work with Dave Anderson, answering a question of Joe Harris from 1987. |

HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR: | Aleksey ZingerStony Brook University |
Enumerative geometry of curves: old and new |

on Tuesday, March 14, 2017, at 3:00 pm in MIT 4-153 | ||

I will present an overview of the (complex) Gromov-Witten invariants and their relation to curve counts provided by Pandharipande's version of Gopakumar-Vafa formula for Fano classes. I will then present a similar formula that transforms the real positive-genus GW-invariants of many real-orientable threefolds into signed counts of curves. These integer invariants provide lower bounds for counts of real curves of a given genus that pass through conjugate pairs of constraints. This talk is based on joint works with P. Georgieva and J. Niu. |

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. |

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. |