Three Problems in the Mathematics of Deep Learning
Explore mathematical concepts behind aligning neural networks with classical programs, including polynomial functors, cohomology, and higher categories.
Characteristic Classes of Étale Local Systems
Explore characteristic classes of étale Z_p-local systems on algebraic varieties, their relation to Chern-Simons classes, and connections to Hodge filtration in p-adic settings.
Characteristic Cycle and Pushforward for L-adic Sheaves
Explore characteristic cycles for l-adic sheaves, their role in measuring ramification, and the compatibility of pushforward along proper morphism in this advanced mathematical lecture.
Secondary Invariants and Arithmetic Rigidity
Explore secondary Chern classes in complex local systems, their definitions, and arithmetic analogs. Delve into rigidity phenomena and motivic speculations in algebraic geometry.
Motives and Ring Stacks
Explore advanced cohomology theories through ring stacks, examining their connection to 6-functor formalism and motivic theory. Gain insights into Tannaka duality and analytic geometry applications.
Birational Invariants from Gromov-Witten Theory - Lecture 2
Explore birational invariants derived from Gromov-Witten theory, focusing on Iritani's theorem and its applications to proving non-rationality of algebraic varieties.
Birational Invariants from Gromov-Witten Theory - Lecture 1
Explore birational invariants derived from Gromov-Witten theory, focusing on Iritani's theorem and its applications to proving non-rationality of geometric objects like cubic 4-folds.
On the Cohomology of Shimura Varieties with Torsion Coefficients
Explore recent advances in Shimura varieties' cohomology with torsion coefficients, including Hodge-Tate period morphism geometry and local-global compatibility insights.
Plectic Cohomology of Mixed Shimura Varieties and Stacks
Explore joint work on plectic cohomology of mixed Shimura varieties and stacks with Tony Scholl from the University of Cambridge.
Introduction to Koszul Duality - Part 3
Explore advanced concepts of Koszul duality, delving into its applications and theoretical foundations in algebraic topology and homological algebra.
Introduction to Koszul Duality - Part 2
Explore advanced concepts of Koszul duality, building on previous knowledge and delving into complex mathematical theories and applications.
Introduction to Koszul Duality - Part 1
Explore Koszul duality fundamentals with Vladimir Dotsenko, delving into algebraic structures and homological algebra concepts.
An Introduction to Rigid Local Systems
Explorez les systèmes locaux rigides, leurs propriétés et applications en géométrie et théorie des nombres. Découvrez les avancées récentes et la conjecture de Simpson sur leur origine géométrique.
Introduction to Circular Orderings - Lecture 2
Explore algebraic and combinatorial aspects of circularly-orderable groups, focusing on cohomology, central extensions, and obstruction spectra. Gain insights through exercises and open problems.
Introduction to Circular Orderings - Lecture 3
Explore algebraic and combinatorial aspects of circularly-orderable groups, focusing on cohomology, left-ordered central extensions, and obstruction spectra. Gain insights through exercises and open problems.
Introduction to Circular Orderings - Lecture 1
Explore algebraic and combinatorial aspects of circularly-orderable groups, covering definitions, group operations, cohomology, and obstruction spectra. Gain insights through exercises and open problems.
Introduction to Circular Orderings - Lecture 4
Explore algebraic and combinatorial aspects of circularly-orderable groups, focusing on cohomology, left-ordered central extensions, and obstruction spectra. Gain insights through exercises and open problems.
The Local Langlands Program and Characteristic p
Explore the local Langlands program for GLn, focusing on representations in characteristic p and recent developments for GL2(K) in p-adic number theory.
Point Counting over Finite Fields and the Cohomology of Moduli Spaces of Curves
Explore algebraic geometry through point counting over finite fields and cohomology of moduli spaces of curves, resolving longstanding questions and confirming Langlands program predictions.
Computing Differentials in the Adams Spectral Sequence and the Last Kervaire Invariant Problem
Explore advanced methods for computing differentials in the Adams spectral sequence and uncover recent progress on the Last Kervaire Invariant Problem in dimension 126.
Introduction to Koszul Duality - Part 5
Explore advanced concepts of Koszul duality, delving into its applications and theoretical foundations in algebraic topology and homological algebra.