CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS HOMOLOGICAL MIRROR SYMMETRY SEMINAR: | Netanel BlaierBrandeis University |
Intro to HMS 2 |

on Thursday, September 29, 2016, at 2:00 - 4:00 pm in CMSA Building, 20 Garden St, G10 | ||

In the second talk, we review (some) of the nitty-gritty details needed to construct a Fukaya categories. This include basic Floer theory, the analytic properties of J-holomorphic curves and cylinders, Gromov compactness and its relation to metric topology on the compactified moduli space, and Banach setup and perturbation schemes commonly used in geometric regularization. We then proceed to recall the notion of an operad, Fukaya's differentiable correspondences, and how to perform the previous constructions coherently in order to obtain $A_\infty$-structures. We will try to demonstrate all concepts in the Morse theory 'toy model'. Time providing, we also discuss orientations. |

THURSDAY SEMINAR: | Jacob LurieHarvard University |
K-Theory of Henselian Rings |

on Thursday, September 29, 2016, at 3:00 - 5:00 pm in Science Center 507 |

GAUGE THEORY, TOPOLOGY, AND SYMPLECTIC GEOMETRY SEMINAR: | Vladimir ChernovDartmouth University |
Minimizing intersection points of loops on a surface and the Andersen-Mattes-Reshetikhin Poisson bracket. (based on a joint work with Patricia Cahn) |

on Friday, September 30, 2016, at 3:30 - 4:30 PM in Science Center 507 | ||

Given two free homotopy classes α1,α2 of loops on an oriented surface, it is natural to ask how to compute the minimum number of intersection points m(α1,α2) of loops in these two classes. We show that for α1≠α2 the number of terms in the Andersen-Mattes-Reshetikhin Poisson bracket of α1 and α2 is equal to m(α1,α2). Chas found examples showing that a similar statement does not, in general, hold for the Goldman Lie bracket of α1 and α2. If time permits we will also discuss the following. Turaev conjectured that his cobracket of a loop is zero if and only if the loop is homotopic to a simple loop. Counterexamples to this conjecture were found by Chas. Cahn modified the Turae'v operation so that the conjecture is true for the modified operation. |

DIFFERENTIAL GEOMETRY SEMINAR: | Alexander LogunovSt. Petersburg & Tel-Aviv |
Zero set of a non-constant harmonic function in R^3 has infinite surface area |

on Tuesday, October 04, 2016, at 4:15 pm in Science Center 507 | ||

Nadirashvili conjectured that for any non-constant harmonic function in R^3 its zero set has infinite surface area. This question was motivated by the Yau conjecture on zero sets of Laplace eigenfunctions. We will give a sketch of the proof of Nadirashvili's conjecture. -- Organized by Prof. Shing-Tung Yau |

NUMBER THEORY SEMINAR: | William Yun ChenInstitute for Advanced Study |
Moduli Interpretations for Noncongruence Modular Curves |

on Wednesday, October 05, 2016, at 3:00 PM in Science Center 507 | ||

Let G be a finite 2-generated group, then we define the notion of a G-structure for elliptic curves, which generalize the classical congruence level structures over Z[1/|G|]. The resulting moduli stacks of elliptic curves with G-structures over C is a union of modular curves, often noncongruence if G is nonabelian. Using the "congruence subgroup property" of SL(2,Z), we deduce that every (non)congruence modular curve is a moduli space of elliptic curves with G-structure. If time permits we will discuss connections with the Inverse Galois Problem and the Unbounded Denominators Conjecture. |

JOINT DEPARTMENT OF MATHEMATICS AND CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX AND PROBABILITY THEORY SEMINAR: | Edgar DobribanStanford University |
Computation, statistics and random matrix theory |

on Wednesday, October 05, 2016, at 3:00 pm in CMSA Building, 20 Garden St, G10 | ||

Random matrices are useful models for large datasets. The Marchenko-Pastur (1967) ensemble for general covariance matrices is an increasingly used modeling framework that captures the effects of correlations in the data, with numerous statistical applications. In this talk we discuss the fruitful interactions between computation, statistics and random matrix theory in this area. We explain a fundamental computational problem in RMT: computing the limit empirical spectral distribution (ESD) of general covariance matrices. Our recent Spectrode method solves this problem efficiently. As an application, we solve a challenging problem in theoretical statistics. We construct optimal statistical tests based on linear spectral statistics to detect principal components below the phase transition. We also describe the software we are building for working with large random matrices, which we hope will broaden reach of RMT. |

CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM: | Alexander LogunovTel Aviv University |
Zeroes of harmonic functions and Laplace eigenfunctions |

on Wednesday, October 05, 2016, at 4:30 PM in CMSA Building, 20 Garden Street, Room G10 | ||

Nadirashvili conjectured that for any non-constant harmonic function in R^3 its zero set has infinite area. This question was motivated by the Yau conjecture on zero sets of Laplace eigenfunctions. Both conjectures can be treated as an attempt to control the zero set of a solution of elliptic PDE in terms of growth of the solution. For holomorhpic functions such kind of control is possible only from one side: there is a plenty of holomorphic functions that have no zeros. While for a real-valued harmonic function on a plane the length of the zero set can be estimated (locally) from above and below by the frequency, which is a characteristic of growth of the harmonic function. We will discuss the notion of frequency, its properties and applications to zero sets in the higher dimensional case, where the understanding is far from being complete. |

SPECIAL SEMINAR: | Nike SunUC Berkeley |
Phase transitions in random constraint satisfaction problems |

on Friday, October 07, 2016, at 3:30 PM in Science Center 507 | ||

I will discuss a class of random constraint satisfaction problems (CSPs), in particular the boolean k-satisfiability (k-SAT) problem. For many random CSP models, heuristic methods from statistical physics yield detailed predictions on phase transitions and other phenomena. This includes the presence of a so-called "replica symmetry breaking" phenomenon, the mathematical understanding of which remains lacking. I will survey some of these heuristics, and describe some progress in the development of mathematical theory for these models. This talk is based on joint works with Jian Ding, Allan Sly, and Yumeng Zhang. |

HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR: | Robert FriedmanColumbia University |
Deformations of cusp singularities |

on Tuesday, October 11, 2016, at 3:00 pm in Science Center 507 | ||

Cusp singularities are a class of normal surface singularities with a rich geometry and deformation theory. In particular their smoothing components are very closely connected to the moduli of certain rational surfaces. In 1981, Looijenga gave a necessary condition for a cusp singularity to be smoothable and conjectured that this condition was also sufficient, a conjecture recently proved by Gross-Hacking-Keel and P. Engel. This talk describes recent joint work with Engel. We define an invariant λ for every semi-stable K-trivial model of a one parameter smoothing of a cusp singularity and show that all possible values of the invariant arise. Using this result, we characterize those rational double point singularities which are adjacent to cusp singularities. |

CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM: | Conan LeungChinese University of Hong Kong |
Coisotropic A-branes and their SYZ transform |

on Wednesday, October 12, 2016, at 4:30 PM in CMSA Building, 20 Garden Street, Room G10 | ||

Kapustin introduced coisotropic A-branes as the natural boundary condition for strings in A-model, generalizing Lagrangian branes and argued that they are indeed needed to for homological mirror symmetry. I will explain in the semiflat case that the Nahm transformation along SYZ fibration will transform fiberwise Yang-Mills holomorphic bundles to coisotropic A-branes. This explains SYZ mirror symmetry away from the large complex structure limit. |

SPECIAL SEMINAR SERIES, JOINT DEPARTMENT OF MATHEMATICS AND CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS: | Masaki KashiwaraRIMS, Kyoto University |
Indsheaves and Riemann-Hilbert correspondence of holonomic D-modules, Part 1 |

on Tuesday, October 18, 2016, at 4:15 - 5:15 pm in Science Center 507 |

DIFFERENTIAL GEOMETRY SEMINAR: | Jonathan ZhuHarvard University |
Entropy and self-shrinkers of the mean curvature flow |

on Tuesday, October 25, 2016, at 3:00 - 4:00 pm *special time in CMSA Building, 20 Garden St, G10 *different location | ||

The Colding-Minicozzi entropy is an important tool for understanding the mean curvature flow (MCF), and is a measure of the complexity of a submanifold. Together with Ilmanen and White, they conjectured that the round sphere minimises entropy amongst all closed hypersurfaces. We will review the basics of MCF and their theory of generic MCF, then describe the resolution of the above conjecture, due to J. Bernstein and L. Wang for dimensions up to six and recently claimed by the speaker for all remaining dimensions. A key ingredient in the latter is the classification of entropy-stable self-shrinkers that may have a small singular set. -- Organized by Prof. Shing-Tung Yau |

SPECIAL SEMINAR SERIES, JOINT DEPARTMENT OF MATHEMATICS AND CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS: | Masaki KashiwaraRIMS, Kyoto University |
Indsheaves and Riemann-Hilbert correspondence of holonomic D-modules, Part 2 |

on Tuesday, October 25, 2016, at 4:15 - 5:15 pm in Science Center 507 |

SPECIAL SEMINAR SERIES, JOINT DEPARTMENT OF MATHEMATICS AND CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS: | Masaki KashiwaraRIMS, Kyoto University |
Indsheaves and Riemann-Hilbert correspondence of holonomic D-modules, Part 3 |

on Tuesday, November 01, 2016, at 4:15 - 5:15 pm in Science Center 507 |