Quadratic Forms and Hermite Constant, Reduction Theory by Radhika Ganapathy
Explores techniques for computing densest lattice packings, including quadratic forms, Hermite constants, and reduction theory. Covers perfect forms, eutactic lattices, and Voronoi's algorithm for listing perfect forms.
Structure of Group Rings and the Group of Units of Integral Group Rings - Lecture 1
Explores group rings, their structure, and units of integral group rings. Covers idempotents, invertible elements, augmentation mapping, and constructions of units including Bass and cyclotomic units.
On Brumer-Stark Units and Hilbert’s 12th Problem by Mahesh Kakde and Samit Dasgupta
Explore Brumer-Stark units and Hilbert's 12th Problem in this advanced number theory lecture, covering Stickelberger's theorem, class field theory, and recent developments in algebraic number theory.
The Finite Part of Infinity by Joseph Samuel
Explore the paradoxical equation 1+2+3...=-1/12, its mathematical interpretation, and its impact on physics, including the Casimir effect, with insights from differential geometry and topology.
The Geometric Langlands Conjecture and Non-Abelian Hodge Theory - Lecture 1
Explore the Geometric Langlands conjecture and non-abelian Hodge theory, examining connections between quantum fields, geometry, and representation theory in modern mathematics and theoretical physics.
Computer-Assisted Proofs in the Arithmetic of Quadratic Forms - IPAM at UCLA
Explore computer-assisted proofs in quadratic forms arithmetic, covering equivalence, representation, local-global principles, and modular forms. Gain insights into complex computations across mathematics.
On the Brumer-Stark Conjecture and Refinements
Exploration of the Brumer-Stark conjecture and its refinements, covering group rings, class groups, and related conjectures in algebraic number theory.
Atsushi Ichino- Theta Lifting and Langlands Functoriality
Explore theta lifting, seesaw identities, and Langlands functoriality in number theory, focusing on modular forms and local Shimura-Waldspurger correspondence.
Mariusz Lemanczyk: Furstenberg Disjointness, Ratner Properties and Sarnak’s Conjecture
Explore Furstenberg disjointness, Ratner properties, and Sarnak's conjecture in number theory and ergodic theory. Delve into multiplicative functions, topological dynamics, and connections to the Chowla conjecture.
Oded Regev: The Reverse Minkowski Theorem
Explore the Reverse Minkowski Theorem, its applications, and open questions in lattice theory with mathematician Oded Regev in this insightful mathematical lecture.
Pseudo-Reductive Groups by Brian Conrad
Explore pseudo-reductive groups with Brian Conrad, covering definitions, properties, and key theorems in this advanced mathematics lecture on algebraic group theory.
The Selberg Sieve and Large Sieve - Lecture 1
Explore the Selberg Sieve and Large Sieve in number theory, covering linear algebra, duality principles, and applications like the Bombieri-Vinogradov theorem in this advanced mathematics lecture.
The Selberg Sieve - Lecture 1
Explore the Selberg sieve method in number theory, covering heuristics, probability, and applications to twin primes. Learn about sieve techniques for detecting primes in sequences.
Paul Arne Østvær- A1 Contractible Varieties
Explore A1 contractible varieties in algebraic geometry, covering cancellation theorems, local model structures, and related proofs in this advanced mathematics lecture.
SRB Measures and Young Towers - Lecture 3 of 4
Explore SRB measures and Young towers in dynamical systems, focusing on nonuniformly hyperbolic systems and their statistical properties. Learn about recent advances in this field of mathematics.
Symbolic Dynamics for Nonuniformly Hyperbolic Systems - Lecture 4
Explore advanced techniques in nonuniformly hyperbolic dynamics, focusing on symbolic coding and statistical properties of complex systems using Markov Partitions and Young Towers.
Symbolic Dynamics for Nonuniformly Hyperbolic Systems - Lecture 3 of 5
Explores advanced techniques in nonuniformly hyperbolic systems, focusing on symbolic dynamics and Markov partitions. Covers key concepts, challenges, and recent developments in the field of dynamical systems.
Symbolic Dynamics for Nonuniformly Hyperbolic Systems - Lecture 2 of 5
Explores advanced techniques in symbolic dynamics for nonuniformly hyperbolic systems, focusing on graph transforms, recurrence properties, and Markov partitions to analyze complex dynamical behaviors.
From Knots to Number Theory II
Explore connections between quantum knot invariants and number theory, covering topics like hyperbolic topology, Kashaev invariant, and quantum modularity. No prior knowledge required.
Modularity of Some Geometric Objects - Definitions, Reasons and State of the Art
Explore zeta functions, L-functions, and Galois representations in geometric objects, focusing on plane projective curves and their conjectured relationships with analytic functions.
The Rogers-Ramanujan Identities and the Icosahedron - Lecture 3
Explore the deep connections between Rogers-Ramanujan identities and the icosahedron, spanning number theory, modular forms, combinatorics, and more. Uncover the beauty and complexity of these mathematical gems.