IITG Mathematics Seminar Series

Lecture Number: | 330 |

Title: | Phantom morphisms and purity |

Speaker: | Prof. Pedro A. Guil Asensio |

Affiliation: | University of Mursia, Spain |

Date: | 19th February, 2019 (Tuesday) |

Time: | 04:00 PM |

Abstract: Phantom morphisms play a central role in Brown Representability Theorem for compactly generated triangulated categories (in particular, the stable module category of K[G], where G is a finite group and K is a field whose characterisic divides the order of the group). In this talk, we will connect this notion with the Theory of Purity of Modules. This will allows us to give a general notion of phantom morphisms connecting two exact structures in addititive categories. We will apply our results to different exact structures. Namely: 1) the pure-exact structure in a Grothendieck category; 2) contractible complexes in Ch(R-Mod); 3) almost split sequences of representations of finite-dimensional algebras; 4) geometrical and categorical purity in the category of quasi-coherent sheaves over a scheme.

Lecture Number: | 329 |

Title: | When averages are extreme: Probabilistic techniques in functional and harmonic analysis |

Speaker: | Prof. Andrew Tonge |

Affiliation: | Kent State University Ohio, USA |

Date: | 11th February, 2019 (Monday) |

Time: | 10:00 AM |

Abstract: In many situations, there is a high probability that the norm of a random polynomial or multilinear form is close to the smallest possible value. We show how some of these situations arise through an interplay of functional and harmonic analysis and illustrate some interesting consequences.

Lecture Number: | 328 |

Title: | Constrained Dynamical System: Rough Paths and Simulation |

Speaker: | Prof. Soumyendu Raha |

Affiliation: | Indian Institute of Science, Bangalore |

Date: | 6th February, 2019 (Wednesday) |

Time: | 4:00 PM |

Abstract: We shall discuss the difficulty in solving and numerically integrating constrained dynamical systems that are naturally modeled as systems of differential-algebraic equations of the form dx/dt = f(x,u),g(x) = 0 where x is in R^n and u is in R^m and m <= n. In this context we shall introduce a horizontal lift and its exponentiation toward construction of a solution. Especially, the solution and behavior of the algebraic variable is of interest. Cases where u can be rough (belong to fractional Holder space) are of interest. A numerical approximation that can produce useful result in computer simulations will be discussed. As an illustration, we shall show how treating stick-slip problems as constrained dynamics, yields interesting results on the time integrating constrained dynamical systems that are naturally modeled as scales of the stick-slip process. In this context we shall study, in particular, the peeling dynamics of an adhesive tape.

Lecture Number: | 327 |

Title: | Through eyes of viscoelastic fluids: How can an external stimulus influence research in theoretical and computational PDEs |

Speaker: | Prof. Amiya Kumar Pani |

Affiliation: | Indian Institute of Technology Bombay |

Date: | 16th January, 2019 (Wednesday) |

Time: | 4:00 PM |

Abstract: Mathematical research is mainly driven by internal questions ( internal to Mathematics). But when it is influenced by questions posed externally, there is no liberty to change the original theme and couple of such questions which are bothering us for the last two decades will be the focus of this talk.In order to understand the context, when mathematical model is formulated to explain approximately certain physical reality, it is important to derive relevant properties mathematically. Say for example in some viscoelastic fluid flows, numerous experiments suggest that after an instantaneous cessation of the external force, the velocity of the fluid dies down with a certain rate. Translating and proving this kind of property pose a challenge in Mathematics research. Starting with a model in a layman's language, in this talk, relevant mathematical issues summarizing our efforts for the last 20-25 years will be briefly discussed. If time permits in the later part of this talk, the focus will be on the following question posed by the user community ` How do we believe the numbers crunched by the machine using an algorithm? Finally, we conclude the talk with some mathematical issues.