On the Algebraic Geometry of Spaces of Persistence Modules
Explore algebraic geometry's application to persistence modules in topological data analysis, offering insights into data structure and shape analysis.
Homological Algebraic Geometry
Explore semiorthogonal decompositions in algebraic geometry, including their properties, geometric significance, and novel applications in categorical constructions and singularity resolutions.
Michel van den Bergh- Noncommutative Crepant Resolutions
Explore noncommutative crepant resolutions in algebraic geometry with Michel van den Bergh, delving into advanced mathematical concepts and their applications.
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.
Counting Lattice Points in Moduli Spaces of Quadratic Differentials
Explore lattice point counting in moduli spaces of quadratic differentials, examining applications in Masur-Veech volumes, geodesic multicurves, and meander enumeration.
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.
Wall-Crossing in Algebraic Geometry
Explore applications of Bridgeland stability conditions and wall-crossing techniques in algebraic geometry, advancing understanding of complex mathematical structures.
David Kazhdan- On the Langlands Correspondence for Curves Over Local Fields
Explores recent results and conjectures on automorphic functions theory for moduli spaces of bundles on curves over local fields, discussing both archimedean and non-archimedean cases.
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.
Evgeny Feigin - PBW Degenerations, Quiver Grassmannians, and Toric Varieties
Explore connections between Lie theory, quiver Grassmannians, and flag variety degenerations, focusing on PBW filtration in highest weight representations and its impact on degenerate flag varieties.
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.
The Balmer Spectrum of Cellular C-Motivic Spectra
Exploration of the Balmer spectrum in cellular C-motivic spectra, focusing on its periodicity (co)sheaf and the C2 group action on formal groups through the [−1]-series.
Equidistribution of Expanding Translates of Curves in Homogeneous Spaces
Explores equidistribution of expanding translates of non-degenerate real-analytic curves in semisimple group spaces, extending previous work and applying to Diophantine approximation on matrices.
Horocycle Flow on Moduli Spaces of Translation Surfaces
Explore the intricate dynamics of horocycle flow on moduli spaces of translation surfaces in this advanced mathematics lecture by Jon Chaika.
Roger Heath Brown - The Determinant Method, Lecture III
Explore variants of the determinant method and its application to consecutive "powerful" numbers in algebraic number theory.
Marina Iliopoulou- Three Polynomial Methods for Point Counting, Lecture III
Explore advanced polynomial techniques for solving geometric problems, including Dvir's method, polynomial partitioning, and slice rank method in finite-field settings.
Roger Heath-Brown- The Determinant Method, Lecture II
Explore the p-adic Determinant Method theorem and its proof in algebraic geometry, advancing understanding of rational points on varieties.
Roger Heath-Brown: The Determinant Method I
Explore rational points on algebraic varieties, their counting methods, and related phenomena in this advanced mathematics lecture by renowned number theorist Roger Heath-Brown.
Valentin Blomer: The Polynomial Method for Point Counting and Exponential Sums
Explore advanced techniques for counting points on curves over finite fields and estimating exponential sums using families of auxiliary polynomials.
The Polynomial Method for Point Counting and Exponential Sums
Explore how auxiliary polynomials aid in counting points on curves over finite fields and estimating exponential and character sums.