Explore advanced mathematical research through this comprehensive seminar series covering diverse areas including algebraic geometry, analysis, number theory, and differential equations. Delve into cutting-edge topics such as composition semigroups on analytic spaces, Vafa-Witten invariants, moduli spaces of sheaves, and free boundary problems. Examine theoretical foundations in areas like P=W correspondence, mirror symmetry, Hopf-Galois extensions, and multiplicative functions in number theory. Investigate geometric problems including hyperkähler manifolds, exotic spheres, closed geodesics, and CMC surfaces, while exploring applications in ergodic theory, probability theory, and potential theory. Study advanced concepts in algebraic geometry such as Quot schemes, cohomology rings, and Cremona groups, alongside analysis topics including elliptic systems, gradient estimates, and reaction-diffusion equations on evolving domains. Gain insights into modern mathematical research through presentations on Finsler manifolds, infinity-Laplacian theory, quasicrystals, and geometric singularities, with special focus on computational aspects of invariants and modular forms.

Syllabus

Composition semigroup on some analytic spaces of the upper half plane
Analysis Seminar "On the number of lower sets with fixed cardinality"
The Euclidean algorithm on number fields and related problems
Weighted A Priori Estimates for Solutions of Uniformly Elliptic Systems
ANALYSIS SEMINAR: Up to the Boundary Gradient Estimates in Bernoulli Type Free Boundary Problems
The variance of a general class of multiplicative functions in short intervals
Hopf-Galois Extensions and Applications
ANALYSIS SEMINAR: Up to the Boundary Gradient Estimates in Bernoulli Type Free Boundary Problems
The variance of a general class of multiplicative functions in short intervals
Mirror symmetry and big algebras
P=W via H_2 (part 2)
P=W via H_2 (part 1)
Introduction to P=W and Mirror symmetry
Lipschitz learning and the infinity-Laplacian
Geometric and multilinear problems in analysis
Algebraic Geometry Seminar - On the geometry of hyperkähler manifolds (Yulieth Prieto Montanez)
On the Riemann zeta-function, Fourier optimization and quadratic forms
Algebraic Geometry Seminars 2022
ICTP Mathematics Colloquium on "More deformations of the cohomology ring of the moduli space of r...
ICTP/IGAP Algebraic Geometry Seminar: Mochizuki's formula and the horizontal Vafa-Witten invariants
Theory of weights in rooted k-trees
ICTP/IGAP seminar on Algebraic Geometry "Computation of the vertical Vafa-Witten invariants II
ICTP/IGAP Algebraic Geometry Seminar "Computation of vertical Vafa-Witten invariants"
ICTP/IGAP Algebraic Geometry Seminar on "Vertical Vafa-Witten invariants and nested Hilbert schemes"
ICTP/IGAP Algebraic Geometry Seminar on "On the cohomology of Quot schemes parametrizing torsion...
ICTP/IGAP Seminar on "Representations of the diagonal and the cohomology rings of Quot schemes"
ICTP/IGAP Algebraic Geometry Seminar on "Vertical Vafa-Witten invariants"
ICTP/IGAP seminar on Algebraic Geometry: Moduli spaces of sheaves, Vafa-Witten formula
ICTP/IGAP seminar on Algebraic Geometry: Refined invariants and Vafa-Witten invariants
ICTP/IGAP seminar on Algebraic Geometry:Representations of the diagonal for moduli spaces of sheaves
ICTP/IGAP seminar : Moduli spaces of sheaves, Vafa-Witten formula and virtual invariants
ICTP/IGAP Virtual invariants of moduli spaces of sheaves on surfaces and Vafa-Witten invariants I
ICTP/IGAP seminar on Algebraic Geometry: The sl(2) action on the Chow ring of an abelian variety
Reversible $d$-dmensional CA over the ring $\mathbb{Z}_m$ and some applications in ergodic theory
BASIC NOTIONS SEMINAR: Orientations in the plane as quantum states
Conditional Measures for the Zero Set of the Gaussian Analytic Function
Probability invariant measure, dynamical partition and hitting times of circle map with singularitie
Math Associates Seminar: Bubbling of Q-curvature equation on 4-manifolds in the null case - MTH
Detecting the completeness of a Finsler manifold via potential theory for its infinity Laplacian
Reaction diffusion equations on evolving domains: regularity and global existence - Math Seminar
Exotic Spheres and Singularities - Math Associates Seminar
Modularity of some geometric objects: definitions, reasons and state of the art
Mating quadratic maps with the modular group
Closed Geodesics on Surfaces without Conjugate Points
Finding solitons in differential geometry
Sampling, tilings, and quasicrystals
Characterization of free boundary CMC surfaces in the ball
Singular chains on Lie groups and the Cartan relations
Symmetries in Algebraic Geometry and the Cremona Group
Joint ICTP/Rio de Janeiro Webinar on Analysis and PDEs "Certainty vs. uncertainty"