Lecture Series in Algebraic Geometry

                                                                                     Lecture Schedules

           Bruhat-Tits group schemes from a geometric perspective and applications to moduli 

                                    by Vikraman Balaji   ( Affiliation : Chennai Mathematical Institute, India )

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 1st Lecture : November 1 , 5 pm - 7 pm IST  ( 11:30 am - 1:30 pm GMT )

2nd Lecture : November 15 , 5 pm - 7 pm IST  ( 11:30 am - 1:30 pm GMT )

3rd Lecture : November 29 , 5 pm - 7 pm IST  ( 11:30 am - 1:30 pm GMT )

Abstract : The aim of these lectures will be to introduce the notion of affine buildings and the notions of parahoric groups. The next aim will be to schematize these notions and get an overview of the structure of the Bruhat-Tits group schemes over discrete valuation rings. I will work entirely on the geometric case of the power series ring in one variable and the valuation ring there. In the last few lectures I will indicate applications of these concepts to the study of torsors on curves. The goal will be to understand the stack of parahoric torsors on smooth projective curves, relate them to the classical stack of parabolic bundles and prove a parahoric generalization of the Mehta-Seshadri theorem.

Notes from first lecture         Notes from second lecture           Notes from third lecture

                                                          Motives of moduli of bundles on curves

                       by Simon Pepin Lehalleur   ( Affiliation : Radboud University Nijmegen, Netherlands )

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 1st Lecture : November 18 , 5 pm - 6:30 pm IST  ( 11:30 am - 1 pm GMT )

2nd Lecture : November 25 , 5 pm - 6:30 pm IST  ( 11:30 am - 1 pm GMT )

3rd Lecture : December 2 , 5 pm - 6:30 pm IST  ( 11:30 am - 1 pm GMT )

4th Lecture : December 9 , 5 pm - 6:30 pm IST  ( 11:30 am - 1 pm GMT )

Abstract : Moduli spaces and stacks of vector bundles are beautiful and central objects in algebraic geometry. Their geometry is very rich but tractable because of its close relationship with the geometry of the underlying curve and simple associated objects like its symmetric powers and its Jacobian. The same is true for closely related moduli on curves: parabolic vector bundles, principal G-bundles, Higgs bundles, etc. . Much is known about the cohomological invariants of these various moduli spaces. I will explain how, in joint works with Victoria Hoskins and Lie Fu, we showed that some of these results can be upgraded to computations in the category of mixed motives of Voevodsky; this both unifies classical computations in cohomology and provides information about algebraic cycles on those moduli spaces. The ultimate goal of the series will be a motivic version of a theorem of Maulik and Shen on the endoscopic decomposition for the moduli of SL_n-Higgs bundles. I will start the lecture series with an introduction to mixed motives. 

References 

Notes from first lecture        Notes from second lecture        Notes from third lecture        Notes from fourth lecture 

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Recording from third lecture    (Passcode: ?SPb6J!! )

Recording from fourth lecture   (Passcode: 9ZRCCo++ )

                          The compactification of the universal moduli space of principal G-bundles

                                    by Angel Luis Muñoz Castañeda  ( Affiliation : Universidad de León, Spain ) 

 1st Lecture : December 10 , 5 pm - 6:30 pm IST  ( 11:30 am - 1 pm GMT )

2nd Lecture : December 17 , 5 pm - 6:30 pm IST  ( 11:30 am - 1 pm GMT )

3rd Lecture : December 24 , 5 pm - 6:30 pm IST  ( 11:30 am - 1 pm GMT )

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Abstract :  Click here 

Notes from first lecture         Notes from second lecture 

Recording from first lecture   (Passcode: zQU0n8#0 )

Recording from second lecture   (Passcode: a8erE9@5 )

Recording from third lecture   (Passcode: 8wb?gK#4 )

                                                Basic revision of Nori's fundamental group scheme 

  by   Jorge Arturo Esquivel Araya  ( affiliation : Universidad de Costa Rica ) 

December 21 , 11:30 am IST ( 6:00 am GMT )

Abstract : A construction of the fundamental group scheme will be reviewed. For this purpose we will talk a little about the category of Essentially finite vector bundles. We will also discuss a functor between G-modules and quasi-coherent sheaves. And we will conclude the construction with a result on Tannakian categories. In addition we will discuss some results on existence, base point dependence and the possibility of base-change of the fundamental group scheme.

                                                                     Instanton Bundles on Fano Threefolds

                                               by     Özhan Genç   ( affiliation : Jagiellonian University , Poland )

April 11 , 3:30 pm IST, Mathematics seminar Hall NAC 522 

Abstract : Click here 

Notes from the lecture 

                                Organizers 

                                          Arijit Dey                                            Sujoy Chakraborty

               (Department of Mathematics, IIT Madras)                         (Postdoctoral fellow, Department of Mathematics, IIT Madras)

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