Vector Delannoy Categories and Further Developments
Exploration of quantum analogues of Delannoy categories, focusing on constructions, properties, and connections to related mathematical concepts in symmetric tensor categories.
The Delannoy Category - Symmetric Tensor Categories and Representation Theory
Explore the Delannoy Category in symmetric tensor theory, featuring classification of simple objects, tensor product rules, and a combinatorial model using Delannoy paths.
The Nil-Brauer Category - Categorification and Applications
Exploration of the nil-Brauer category, its relation to quantum groups, and applications in categorification and Soergel bimodules, presented by Jonathan Brundan at IPAM's workshop.
Low Rank Symmetric Fusion Categories in Positive Characteristic
Explore classification of symmetric fusion categories in positive characteristic, focusing on low-rank cases and the second Adams operation's role in obtaining classification results.
Tannakian Radical and Mantle of a Braided Fusion Category
Explore Tannakian radical and mantle concepts in braided fusion categories, their properties, and applications in classification theory with mathematician Dmitri Nikshych.
The Extended Freudenthal Magic Square via Tensor Categories
Explore unital composition superalgebras and their connection to the Extended Freudenthal Magic Square in characteristic 3, using symmetric tensor categories and representation theory.
Polynomial Superfunctors - Applications to Finite Supergroup Schemes
Explore polynomial superfunctors and their applications in finite supergroup schemes. Gain insights into cohomology calculations and recent developments in representation theory.
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.
Growth and Tensor Products in Representation Theory - Lecture 1
Explore asymptotic counting of summands in tensor products of representations, with numerous examples to illustrate concepts in symmetric tensor categories and representation theory.
Border Subrank of Tensors
Exploration of tensor subrank and border subrank, including construction of maximal border subrank tensors and lower bound computation for the dimension of maximal border subrank tensor sets.
From Moments to Matrices
Explore the fascinating connection between moments and matrices in this engaging lecture by mathematician John Urschel, delving into advanced mathematical concepts and their applications.
Small Ball Probabilities for Random Tensors and Analysis of Tensor Decompositions
Explore sharp anticancellation inequalities for simple random tensors and their applications in tensor reconstruction algorithms, presented by Grigoris Paouris at IPAM's Tensor Networks Workshop.
Heights on Character Varieties, Free Subgroups and Spectral Gaps by Emmanuel Breuillard
Explore heights on character varieties, free subgroups, and spectral gaps in this advanced mathematics lecture, delving into Zariski dense subgroups and their applications in geometry and number theory.
Positivity and Higher Teichmüller Spaces
Explore positivity in Lie groups, positive representations, and their connected components. Delve into Hitchin's Teichmüller components and related open questions in higher Teichmüller theory.
Singular Value Decomposition with R - Introduction to Text Analytics with R Part 8
Learn to perform truncated SVD, project TF-IDF vectors into semantic space, compare decision tree and random forest models, and explore random forest tuning using R packages like irlba and caret for text analytics.
Galois Groups of Lacunary Sparse Polynomial Systems
Explore Galois groups in lacunary sparse polynomial systems, examining their properties and applications in algebraic geometry and number theory.
Commutative Algebra to Representation Theory Through the Combinatorics of Filtered RSK
Explore connections between commutative algebra and representation theory via combinatorial analysis of filtered Robinson-Schensted-Knuth algorithm.
Schubert Problems of Types A and C in Macaulay2
Explore Schubert problems in types A and C using Macaulay2, focusing on computational approaches in enumerative geometry and algebraic combinatorics.
Right-Angled Artin Subgroups of Graph Braid Groups
Explore right-angled Artin subgroups in graph braid groups, examining recent conjectures and their applications to topological complexity in algebraic topology.
On the Geometry of Uniform Meandric Systems
Exploring the geometry of meandric systems, focusing on a century-old question about loop crossings. Presents a conjecture on large-scale geometry and related rigorous results.
Spectrum of Random-to-Random Shuffling in the Hecke Algebra
Explore the elegant eigenvalue formulas of random-to-random shuffling and its generalization to the Hecke algebra, with insights into Markov chains and algebraic combinatorics.