CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM: | Simona CoccoCNRS & Ecole Normale Supérieure, Paris, France |
Reverse modeling of protein sequence data: from graphical models to structural and functional predictions. |

on Tuesday, May 02, 2017, at 4:00pm in CMSA Building, 20 Garden St, G10 | ||

A fundamental yet largely open problem in biology and medicine is to understand the relationship between the amino-acid sequence of a protein and its structure and function. Protein databases such as Pfam, which collect, align, and classify protein sequences into families containing similar (homologous) sequences are growing at a fast pace thanks to recent advances in sequencing technologies. What kind of information about the structure and function of proteins can be obtained from the statistical distribution of sequences in a protein family? To answer this question I will describe recent attempts to infer graphical models able to reproduce the low-order statistics of protein sequence data, in particular amino acid conservation and covariation. I will also review how those models have led to substantial progress in protein structural and functional predictions. |

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. |

JOINT DEPT OF MATHEMATICS AND CENTER OF MATHEMATICAL SCIENCES & APPLICATIONS RANDOM MATRIX AND PROBABILITY THEORY SEMINAR: | Ilya SoloveychikHarvard School of Engineering & Applied Sciences |
Deterministic Random Matrices |

on Wednesday, May 03, 2017, at 3:00 pm in CMSA Building, 20 Garden St, G10 | ||

In many applications researchers and engineering need to simulate random symmetric sign (+/-1) matrices (Wigner's matrices). The most natural way to generate an instance of such a matrix is to toss a fair coin, fill the upper triangular part of the matrix with the outcomes and reflect it part into the lower triangular part. For large matrix sizes such approach would require a very powerful source of randomness due to the independence condition. In addition, when the data is generated by a truly random source, atypical non-random looking outcomes have non-zero probability of showing up. Yet another issue is that any experiment involving tossing a coin would be impossible to reproduce exactly, which may be crucial in computer scientific applications. In this talk we focus on the problem of generating n by n symmetric sign matrices based on the similarity of their spectra to Wigner's semicircular law. We develop a simple completely deterministic construction of symmetric sign matrices whose spectra converge to the semicircular law when n grows to infinity. The Kolmogorov complexity of the proposed algorithm is as low as 2 log (n) bits implying that the real amount of randomness conveyed by the semicircular property is quite small. |

CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM: | Xue-Mei LiUniv. of Warwick |
Perturbation to conservation law and stochastic averaging |

on Wednesday, May 03, 2017, at 4:30 PM in Science Center 507 | ||

A deterministic or random system with a conservation law is often used to approximate dynamics that are also subjected to smaller deterministic or random influences. Consider for example dynamical descriptions for Brownian motions and singular perturbed operators arising from rescaled Riemmannian metrics. In both cases the conservation laws, which are maps with values in a manifold, are used to separate the slow and fast variables. We discuss stochastic averaging and diffusion creation arising from these contexts. Our overarching question is to describe stochastic dynamics associated with the convergence of Riemannian manifolds and metric spaces. |

GAUGE THEORY, TOPOLOGY AND SYMPLECTIC GEOMETRY SEMINAR: | Daniel Cristofaro-GardinerHarvard University |
Two or infinity |

on Friday, May 05, 2017, at 3:30 - 4:30 pm in Science Center 507 | ||

A central goal in symplectic and contact geometry is to better understand the dynamics of “Reeb” vector fields. About a decade ago, Taubes showed that any Reeb vector field on a closed three-manifold has at least one closed orbit. I will discuss recent joint work showing that, under some hypotheses, any Reeb vector field on a closed three-manifold has either two, or infinitely many, closed orbits. Key tools are an identity relating the lengths of certain sets of Reeb orbits to the volume of the three-manifold, and the theory of global surfaces of section as developed by Hofer, Wysocki, and Zehnder. |

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. |