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Graduate Summer School on the Geometry and Modular Representation Theory of Algebraic Groups: August 19 – 23, 2019

 
Organized by Mark Andrea de Cataldo, Francois Greer, Christian Schnell

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Shuttle Schedule – RTG Graduate Summer School

 
The goal of this summer school is to introduce Ph.D. students and Postdocs to exciting recent developments in the geometry of algebraic groups and in modular representation theory. 
 
The school will consist of two morning lecture series and of afternoon lectures on topics directly related to the morning lecture series.
Michel Brion (Grenoble) will give one lecture series on the “Structure of algebraic groups and geometric applications”. Geordie Williamson (Sydney) will give the other lecture series  “On the modular representation theory of algebraic groups.”  
M. Brion’s abstract. The course will first give an overview of the “classical” structure theory of algebraic groups and of some related geometric developments and problems;
for example, on automorphism groups of projective algebraic varieties.
It will then address results and questions on algebraic groups over arbitrary fields, including the structure of pseudo-reductive groups (work of Conrad, Gabber and Prasad), and of pseudo-abelian varieties (Totaro). Five lectures, 75 minutes each.
G. Williamson’s abstract. This course will be about the modular (i.e. characteristic p) representation theory of reductive algebraic groups, like the general linear and symplectic groups. I will begin by reviewing the algebraic theory, where there are beautiful connections to classical Lie theory and finite group theory. I will then pass to the geometric theory (perverse and parity sheaves) which is behind recent breakthroughs in the subject. The theory is rich in mysteries and open conjectures, and I will try to outline potentially interesting research directions. Five lectures, 75 minutes each.

Talk Schedule


Time Title Speaker Location
9:00am Geometric and modular representation of algebraic groups, I G. Williamson SCGP 102
10:15am Coffee Break N/A SCGP Cafe
10:45am Structure results for algebraic groups over algebraically closed fields M. Brion SCGP 102
1:45pm Kazhdan-Lusztig polynomials V. Gouttard SCGP 102
2:45pm Commutative algebraic groups over algebraically closed fields B. Wu SCGP 102
3:30pm Coffee Break N/A SCGP Cafe

Time Title Speaker Location
9:00am Structure of anti-affine groups and applications M. Brion SCGP 102
10:15am Coffee Break N/A SCGP Cafe
10:45am Geometric and modular representation of algebraic groups, II G. Williamson SCGP 102
1:45pm Homogeneous vector bundles over abelian varieties M-T. Trinh SCGP 102
2:45pm Stalks of intersection cohomology complexes on the flag variety T. Chatterjee SCGP 102
3:30pm Coffee Break N/A SCGP Cafe

Time Title Speaker Location
9:00am Geometric and modular representation of algebraic groups, III G. Williamson SCGP 102
10:15am Coffee Break N/A SCGP Cafe
10:45am Algebraic groups over arbitrary fields M. Brion SCGP 102
1:45pm The geometric Satake equivalence D. Kubrak SCGP 102
2:45pm Unipotent groups in positive characteristics P. Boixeda-Alvarez SCGP 102
3:30pm Coffee Break N/A SCGP Cafe

Time Title Speaker Location
9:00am Pseudo-abelian varieties M. Brion SCGP 102
10:15am Coffee Break N/A SCGP Cafe
10:45am Geometric and modular representation of algebraic groups, IV G. Williamson SCGP 102
1:45pm An overview of the structure of pseudo-reductive groups J. Baine SCGP 102
2:45pm Connections to the Local Langlands correspondence J. Fintzen SCGP 102
3:30pm Coffee Break N/A SCGP Cafe

Time Title Speaker Location
9:00am Geometric and modular representation of algebraic groups, V G. Williamson SCGP 102
10:15am Coffee Break N/A SCGP Cafe
10:45am Complete homogeneous varieties over an arbitrary field M. Brion SCGP 102
12:00pm Lunch N/A SCGP Cafe