
Explore connections between non-negative integer sets and diverse geometries, examining functions associated with primitive integer vectors and their relation to convex, toric, and birational geometries.

Explore magnitude and path homology concepts with mathematician Sergei Ivanov, delving into homological algebra, algebraic topology, and simplicial homotopy theory.

Explore harmonic maps with free boundary, covering existence, regularity, and parabolic blow-up. Examine elliptic and parabolic problems, recent advances in regularity theory, and geometric applications to the Steklov problem.

Explore quantitative cobordism in topology, focusing on non-constructive existence proofs and connections to geometry. Delve into Manin's principle, Cheeger-Gromov heuristic, and manifold constructions.

Explore homotopy groups of spheres, their computational methods, and recent advancements in topology using motivic homotopy theory and related techniques.

Explore linear stability of compact shrinking Ricci solitons, including positive Einstein manifolds. Examine critical aspects, open problems, and recent research findings in Ricci flow and geometric analysis.

Explore quantitative stability of Sobolev inequalities, focusing on Struwe's decomposition and recent advancements in dimensional-dependent estimates for multiple bubbles in various dimensions.

Explore recent advancements in the existence theory of minimal and constant mean curvature surfaces, surveying cutting-edge developments in this mathematical field.

Explore developments in enumerative geometry on Calabi-Yau 4-folds, including point counting, curve counting, and surface counting, with connections to string theory and physics.

Explore groundbreaking research on Kakeya sets in R^3, uncovering a new lower bound for Hausdorff dimension and its implications in geometric measure theory.

Explore the local Langlands program for GLn, focusing on representations in characteristic p and recent developments for GL2(K) in p-adic number theory.

Explore algebraic geometry through point counting over finite fields and cohomology of moduli spaces of curves, resolving longstanding questions and confirming Langlands program predictions.

Explore integrable billiards and the Birkhoff-Poritsky conjecture, focusing on Hopf-type rigidity and its extension to Twist symplectic maps and billiards.

Explore divisibility of spheres with measurable pieces, focusing on Euclidean (d-1)-dimensional sphere S^(d-1) and special orthogonal matrices. Examine impossibility of measurable divisibility for generic rotations.

Explore the biautomaticity of Coxeter groups and its implications for uniform lattices in building isometry groups. Gain insights from recent mathematical research.

Explorez les groupes libres-par-cycliques et leurs quotients finis. Découvrez les résultats récents sur la distinction de ces groupes par leurs quotients finis dans le cadre de la géométrie combinatoire.

Explore sharp stability in the Brunn-Minkowski inequality for arbitrary sets, delving into combinatorics and its connections with metric geometry and analysis.

Explore exponential decay of intersection volume and its applications in extremal and probabilistic combinatorics with distinguished researcher Hong Liu.

Explore geometric applications of linear algebra with János Pach, covering discrete geometry, convexity, and combinatorics in this research seminar.

Explore spherical functions and mirror symmetry in mathematics, bridging quantum physics and the Langlands Program through innovative interdisciplinary approaches.

Explore geometric representation theory, super groups, and non-commutative algebraic geometry with a focus on Schobers and Riemann-Hilbert correspondence.