Javier Arsuaga - Applications of Computational Topology to the Analysis of Breast Cancer
Explore computational topology's role in breast cancer analysis, uncovering new insights through advanced mathematical techniques and data visualization methods.
Peter Bubenik - Statistical Topological Data Analysis
Explore statistical methods for analyzing topological data, combining mathematical concepts with practical applications in data science and machine learning.
Vin de Silva - Functors and Cosheaves for Topological Persistence
Explore functors and cosheaves in topological persistence, delving into advanced concepts of applied algebraic topology and their applications in data analysis.
Amit Patel - Generalized Persistence Diagrams
Explore generalized persistence diagrams in algebraic topology, examining their applications and theoretical foundations for advanced data analysis and topological insights.
Topology and Combinatorics of Fair Division
Explore the intersection of topology and combinatorics in fair division problems, examining mathematical techniques for equitable resource allocation and distribution.
Tropical Coordinates on the Space of Persistence Barcodes
Explore tropical coordinates in persistence barcodes, a key concept in applied algebraic topology, and their applications in data analysis and shape recognition.
Chad Giusti - Topology and Neural Computation
Explore the intersection of topology and neural computation, examining how mathematical concepts can enhance our understanding of brain function and artificial intelligence.
Multidimensional Persistence
Explore multidimensional persistence in algebraic topology, examining advanced concepts and applications in data analysis and shape recognition.
Sausages and Butcher Paper
Explore geometric principles through everyday objects, unraveling complex mathematical concepts with accessible examples and innovative visualizations.
Entropy in Mean Curvature Flow
Explore entropy in hypersurfaces and its role in mean curvature flow. Survey recent progress on conjectures about sharp lower bounds and extensions in geometric complexity.
Joel Kamnitzer- Perfect Bases in Representation Theory- Three Mountains and Their Springs
Exploration of perfect bases in representation theory, examining three approaches and their combinatorial implications for tensor product multiplicities in semisimple groups.
On Ulam's Problem 19 and Related Problems - IPAM at UCLA
Explore uniqueness problems related to Ulam's Problem 19 from the Scottish book, presented by Dima Ryabogin at IPAM's Calculus of Variations workshop.
Quantitative Stability in Geometric and Functional Inequalities - IPAM at UCLA
Explore geometric and functional inequalities in analysis and geometry, focusing on their validity and minimizer structures. Gain insights into recent developments in this fascinating field.
On a Conjectural Symmetric Version of the Ehrhard Inequality
Explores a conjectural symmetric version of Ehrhard's inequality for Gaussian measures, discussing minimizers, equality cases, and connections to Brascamp-Leib inequality on convex sets.
Size of Line Intersections in High Dimensional L_p-Balls and Product Measures
Explore high-dimensional geometry with Bo'az Klartag as he discusses line intersections in L_p-balls and product measures, examining the isodiametric inequality and its implications.
Groups Acting on Hyperbolic Spaces - A Survey
Explore group actions on hyperbolic spaces with Mladen Bestvina in this comprehensive survey, covering key concepts, recent developments, and applications in geometric group theory.
The Geometry of Geometries - Matroid Theory, Old and New
Explore matroid theory's origins, connections, and recent geometric advances in combinatorial mathematics, highlighting matroid polytope, Bergman fan, and conormal fan models.
A Survey Lecture on Billiards
Explore the fascinating world of mathematical billiards with Richard Evan Schwartz in this engaging survey lecture on dynamical systems and geometry.
Jacob Rasmussen - Floer Homology of 3-Manifolds with Torus Boundary
Explore advanced concepts in Floer homology, focusing on 3-manifolds with torus boundary. Gain insights into cutting-edge mathematical research and its applications in topology.
Homological Knot Invariants from Mirror Symmetry
Explore homological knot invariants through the lens of mirror symmetry, delving into advanced mathematical concepts and their interconnections in topology and geometry.
Variational Proofs of Isoperimetric Inequalities
Explore variational proofs of isoperimetric inequalities, their generalizations, and open problems in this advanced mathematics lecture by Steven Heilman at IPAM's workshop.