q-series, Resurgence and Modularity
Explore q-series, resurgence, and modularity in quantum modular forms, focusing on Ramanujan's σ(q) series and its connections to other mathematical structures.
A Conjectural Reciprocity Law for Realizations of Motives
Explore a conjectural reciprocity law connecting realizations of motives, drawing parallels to classical number theory and expanding on Hodge theory's comparison isomorphisms.
Geometry, Arithmetic, and Dynamics of Discrete Groups - Lecture 4
Explore advanced concepts in discrete group theory, focusing on geometric, arithmetic, and dynamic aspects with Professor Nikolay Bogachev from the University of Toronto.
Local Fields in Lean
Explore local fields using the Lean theorem prover, focusing on mathematical foundations and practical applications in number theory and algebraic geometry.
New Pi Formula Discovery - Interview with Sinha and Saha
Interview with physicists who discovered a new formula for Pi, discussing their groundbreaking research and its implications for mathematics and physics. Insights into the process of scientific discovery and collaboration.
The Multiple Membrane Problem
Explore the N-membranes problem in mathematics, focusing on equilibrium positions of ordered elastic membranes and their free boundary regularity.
Geometric Variational Problems: Regularity vs Singularity Formation
Explore techniques for existence, regularity, and singularity formation in geometric problems, focusing on harmonic maps, Yang-Mills connections, and nematic liquid crystals. Learn about new gluing methods for parabolic flows.
The High-Degree Rational Cohomology of the Special Linear Group
Explore high-degree rational cohomology of SL_n(Z) and SL_n(R) for number rings. Examine Steinberg modules and associated simplicial complexes to understand special linear group cohomology.
Counting Curves in Calabi-Yau Threefolds
Explore enumerative invariants and a universal approach to counting curves in Calabi-Yau threefolds. Discover how cluster formalism aids computations and potentially simplifies conjectural identities between invariants.
Computing the Weil Representation of Superelliptic Curves
Explore the Weil representation of superelliptic curves, focusing on local Galois representations and stable reductions in algebraic geometry.
Counting Arithmetic - A New Foundational Approach
Explore a new foundational approach to arithmetic centered on counting, challenging traditional views and introducing a novel interpretation of arithmetical equations.
The Congruent Number Problem
Explore the ancient congruent number problem and its connection to the Birch and Swinnerton-Dyer conjecture, one of mathematics' most challenging millennium problems.
On a Function of G.H. Hardy and J.E. Littlewood
Explore Hardy and Littlewood's series expansion, its broader context, and connections to Beurling's theorem and ternary quadratic forms' zeta functions.
Point-Counting and the Zilber-Pink Conjecture - Lecture 4
Explore the Zilber-Pink conjecture, its relation to classical conjectures, and point-counting strategies for proving cases, focusing on curves in modular curve powers.
Outliers of Perturbations of Banded Toeplitz Matrices
Explore outlier eigenvalues of perturbed banded Toeplitz matrices, focusing on their behavior in regions outside the limiting spectral distribution's support as matrix size increases.
Point-Counting and the Zilber-Pink Conjecture - Lecture 3
Explore the Zilber-Pink conjecture, its relation to classical conjectures, and point-counting strategies for proving cases, focusing on curves in modular curve powers.
Revised GCH or Would Cantor Have Understood - A Contemporary Perspective on the Continuum Hypothesis
Explore the Continuum Hypothesis and its philosophical implications in set theory. Examine contemporary perspectives on Cantor's famous postulate and its generalized form.
Remarks about Cantor's Theorem
Explore Cantor's Theorem and its implications for infinite cardinalities. Examine the historical context, compare proofs, and discover applications to paradoxical mathematical situations.
Barry Mazur and the Infinite Cheese of Knowledge - A Mathematical Documentary
Explore the life and insights of influential mathematician Barry Mazur in this intimate documentary, capturing his wit, profound approach to mathematics, and enduring impact on the field.
Prime, Knots and the Adele Class Space
Explore geometric connections between primes and knots through scaling site theory, adele class space, and finite abelian extensions of Q, revealing insights into number theory and topology.
Analytic Stacks - Lecture 12
Explore new foundations for analytic geometry, covering light condensed abelian groups, analytic rings, analytic stacks, and examples with renowned mathematician Peter Scholze.