Donaldson-Thomas and Gromov-Witten Theories - Part 9
Explore moduli spaces of algebraic curves and coherent sheaves, their invariants, and connections to geometry, topology, and string theory. Includes computations of Gromov-Witten and Donaldson-Thomas invariants.
Mathematics - The Language of Nature
Explore symmetry's role in math and physics with Edward Frenkel, delving into the Langlands program and its potential for unifying mathematical theories in this engaging lecture.
Euler's and Fermat's Last Theorems, the Simpsons and CDC6600
Explore Fermat's last theorem, Euler's conjecture, and their connections to pop culture and computing history. Delve into mathematical proofs and historical insights.
Ramanujan - Making Sense of 1+2+3+... = -1/12 and Co.
Explore the mathematical paradox of infinite sums equaling unexpected values, delving into Ramanujan's work, summation rules, and connections to the Riemann Zeta function.
Generalized Riemann Hypothesis and Brownian Motion - Giuseppe Mussardo
Explore the fascinating connection between number theory and physics, focusing on the Riemann Hypothesis and its relation to Brownian motion through statistical physics perspectives.
David Loeffler, Sarah Zerbes - Euler Systems and the Bloch-Kato Conjecture for Automorphic
Explore Euler systems and the Bloch-Kato conjecture in relation to automorphic forms, delving into advanced mathematical concepts and their applications.
The Cohomology of Shimura Varieties with Torsion Coefficients and Applications
Explore Shimura varieties' cohomology with torsion coefficients and its applications in advanced mathematics, presented by Ana Caraiani.
Marie-France Vignéras- Modular Representations of P-Adic Groups
Explore modular representations of p-adic groups in the Langlands program, examining their connections to number theory and geometry using various vector spaces and modules.
The Distribution of Values of Zeta and L-Functions
Explore the intricate world of zeta and L-functions, delving into their value distribution patterns and mathematical implications with renowned number theorist Kannan Soundararajan.
Probability Theory for Random Groups Arising in Number Theory
Explores probability theory for random groups in number theory, topology, and combinatorics. Covers moment problems, universality theorems, and distributions of class groups and Selmer groups.
Arithmetic Dynamics - A Survey
Explore arithmetic dynamics, a field merging number theory and algebraic geometry with dynamical systems, examining key problems and recent advancements in this emerging area of mathematics.
30 Years of Modularity - Number Theory Since the Proof of Fermat's Last Theorem
Explore advancements in number theory since Fermat's Last Theorem, focusing on modularity and its impact on mathematical research over the past three decades.
Olivier Wittenberg- Some Aspects of Rational Points and Rational Curves
Explore rational points and curves in algebraic geometry, examining their properties and connections to other mathematical concepts.
Classification of Modular Fusion Categories - Part 1 of 2 - IPAM at UCLA
Explore unitary modular tensor categories and their role in classifying topological phases of matter, covering known results, open problems, and techniques from various mathematical fields.
Points on Shimura Varieties Modulo Primes
Explore the intricacies of Shimura varieties modulo primes, delving into advanced mathematical concepts and their applications in number theory and algebraic geometry.
Dimitris Koukoulopoulos: Rational Approximations of Irrational Numbers
Explore rational approximations of irrational numbers with Dimitris Koukoulopoulos, delving into mathematical concepts and techniques for understanding these complex relationships.
The Number of Rational Points on a Curve of Genus at Least Two
Explore the intriguing mathematical concept of rational points on higher genus curves, delving into advanced number theory and algebraic geometry.
Jacob Lurie: A Riemann-Hilbert Correspondence in P-adic Geometry
Explore p-adic geometry and the Riemann-Hilbert correspondence, covering perfectoid spaces, crystals, and spectral methods in this advanced mathematics lecture.
Jonathan Hickman- On Littlewood-Paley Theory for Space Curves
Explore Littlewood-Paley inequalities for functions with Fourier transforms near submanifolds, focusing on space curves and applications in harmonic analysis, PDE, and number theory.
Osama Khalil- Diophantine Approximation on Fractals and Homogeneous Flows
Explore Diophantine approximation on fractals and homogeneous flows, examining exceptional sets and their connections to recurrence behavior. Discover new results on Hausdorff dimension of divergent orbits and self-similar measure projections.
Equidistribution of Linear Random Walks on the Torus
Explores quantitative equidistribution for linear random walks on the torus, presenting recent progress relaxing the proximality assumption in Bourgain et al.'s work. Joint research with Nicolas de Saxcé.