Depth Reductions of Multiple Polylogarithms - State of the Art Around Goncharov's Depth Conjecture
Explore depth reductions of multiple polylogarithms, focusing on Goncharov's Depth Conjecture and recent advancements in proving related identities and reductions.
Modular Regulators and Multiple Modular Values
Explore recent advancements in computing Goncharov regulator integrals for K_4 classes on modular curves, relating them to multiple modular values and single L-values of modular forms.
Fourier Uniformity of Multiplicative Functions
Explore Fourier uniformity of multiplicative functions, its connection to prime number distribution, and related conjectures like Chowla and Sarnak in this advanced mathematics lecture.
Integer Points on Mordell Curves
Explore integer solutions on Mordell curves, a fascinating topic in number theory. Gain insights into this complex mathematical concept through clear explanations and examples.
Iwasawa Theory of Isogeny Graphs With Level Structures
Explore advanced number theory concepts, focusing on Iwasawa theory and its application to isogeny graphs with level structures in this specialized mathematics seminar.
Proof of the Geometric Langlands Conjecture
Explore recent breakthroughs in the geometric Langlands conjecture, including its proof in characteristic zero settings, framework, obstacles, and solutions in this advanced mathematics lecture.
Chinese Remainder Theorem and Carlson's Theorem for Monoidal Triangulated Categories
Explore Carlson's connectedness theorem generalization for monoidal triangulated categories, including a Chinese remainder theorem version and Balmer support properties.
Local-Global Principles for Norm One Tori and Multinorm Tori Over Semi-Gl
Explore local-global principles for norm one tori and multinorm tori over semi-global fields, delving into advanced algebraic number theory and geometric applications.
Q Series via Box Arithmetic - Math Foundations 239
Explore q-series through innovative "box arithmetic," offering a fresh perspective on algebra, analysis, combinatorics, and number theory with computational advantages and philosophical insights.
Introduction to Bruhat-Tits Theory - Lecture 1
Comprehensive introduction to Bruhat-Tits theory, exploring its foundations and applications in algebraic groups and number theory. Ideal for advanced mathematics students and researchers.
Bounded Generation of Linear Groups and Diophantine Approximation - Lecture 1
Explore Zariski-dense subgroups, number theory, and geometric applications in this lecture on bounded generation of linear groups and Diophantine approximation.
Orbit Closures on Homogeneous Spaces and Applications to Number Theory by George Tomanov
Explore orbit closures on homogeneous spaces and their applications to number theory in this advanced mathematics lecture by George Tomanov, part of a program on Zariski dense subgroups.
Beyond the Riemann Hypothesis - Numberphile
Explore advanced mathematical concepts beyond the Riemann Hypothesis with Jared Duker Lichtman. Delve into prime numbers, complex analysis, and cutting-edge research in number theory.
On the Hardy Littlewood 3-Tuple Prime Conjecture and Convolutions of Ramanujan Sums
Explore the Hardy-Littlewood 3-tuple prime conjecture and its connections to Ramanujan sum convolutions in this advanced number theory seminar by Shivani Goel from IIIT-Delhi.
Solving a Higher Degree Diophantine Equation
Explore techniques for solving complex Diophantine equations of higher degrees, enhancing problem-solving skills in number theory and algebraic manipulation.
Arithmetic Field Theory for Elliptic Curves by Minhyong Kim
Explore advanced arithmetic field theory for elliptic curves, focusing on rational points on modular curves, Chabauty methods, and computational aspects in arithmetic geometry.
Counting Rational Points on Modular Curves of Genus 0 Over Number Fields by Peter Bruin
Explore techniques for counting rational points on modular curves of genus 0 over number fields, advancing understanding in arithmetic geometry and algebraic number theory.
Diophantine Stability for Elliptic Curves on Average by Anwesh Ray
Explore Diophantine stability for elliptic curves, focusing on average-case analysis. Gain insights into arithmetic geometry and modular curves through advanced theoretical and computational approaches.
A Simple Dichotomy in Serre's Uniformity Question by Davide Lombardo
Explore Serre's Uniformity Question in arithmetic geometry, focusing on rational points on modular curves and their implications for elliptic curves and number theory.
A Chabauty-Coleman-Caro-Pasten Bound in Higher Dimensions by Netan Dogra
Explore advanced techniques in arithmetic geometry, focusing on rational points on modular curves and higher-dimensional varieties using Chabauty-Coleman-Caro-Pasten methods.
Collaborating with Mathematicians on Major Societal Challenges - Session B02
Explore interdisciplinary collaborations between mathematicians and physicists addressing societal challenges, from quantum computing to climate science, through talks by leading researchers.