DIFFERENTIAL GEOMETRY SEMINAR: | Yong LinRenmin University |
Heat kernel estimate and solution of semi linear heat equations on graphs |

on Tuesday, January 24, 2017, at 4:15 pm in Science Center 507 | ||

We prove the heat kernel lower estimate on graphs under volume growth condition. By using this heat kernel estimate and curvature assumption, we prove the existence and nonexistence results of global solutions for the semilinear heat equation on graphs. --Organized by Professor Shing-Tung Yau |

CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MATHEMATICAL PHYSICS SEMINAR: | Yu QiuChinese University of Hong Kong |
Spherical twists on 3-Calabi-Yau categories of quivers with potentials from surfaces and spaces of stability conditions |

on Monday, January 30, 2017, at 12:00 pm in CMSA Building, 20 Garden St, G10 | ||

We study the 3-Calabi-Yau category D(S) associated to a marked surface S. In the case when S is unpunctured, we show that the spherical twist group, which is a subgroup of auto-equivalence group of D(S), is isomorphic to a subgroup of the mapping class group of S_Delta--the decorated version of S. In the case when S is an annulus, we prove that the space Stab of stability conditions on D(S) is contractible. We also present working progress on proving the simply connectedness of Stab for any unpunctured case and on studying Stab for the punctured case. |

DIFFERENTIAL GEOMETRY SEMINAR: | Yu QiuChinese University of Hong Kong |
Stability conditions for quivers via exchange graphs |

on Tuesday, January 31, 2017, at 4:15 pm in Science Center 507 | ||

Let Q be an acyclic quiver and D_N(Q) be the associated N-Calabi-Yau category. We (with Alastair King) show that the quotient graph of the exchange graph of hearts/t-structures in D_N(Q) by the spherical twists is isomorphic to the (N-1)-cluster exchange graph. In the case when Q is of Dynkin type, we (with Jon woolf) show that the spherical twist group is isomorphic to the braid group of Q and the corresponding (principal component of) space of stability conditions is contractible. Organized by Prof. Shing-Tung Yau |

CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM: | Sean EddyHarvard Dept of Molecular and Cellular Biology |
Biological sequence homology searches: the future of deciphering the past |

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

Computational recognition of distant common ancestry of biological sequences is a key to studying ancient events in molecular evolution. The better our sequence analysis methods are, the deeper in evolutionary time we can see. A major aim in the field is to improve the resolution of homology recognition methods by building increasingly realistic, complex, parameter-rich models. I will describe current and future research in homology search algorithms based on probabilistic inference methods, using hidden Markov models (HMMs) and stochastic context-free grammars (SCFGs). We make these methods available in the HMMER and Infernal software from my laboratory, in collaboration with database teams at the European Bioinformatics Institute in the UK. |