The Combinatorics of Finite Simple Groups - ICBS 2024
Explore the interplay between finite simple groups, combinatorics, and group theory, examining recent developments and introducing algebraic tools for geometric structures.
Multivariable (φ, Γ)-Modules and Local-Global Compatibility
Explore multivariable $(\varphi, \Gamma)$-modules, extending Colmez's construction to $\mathrm{GL}_2(K)$ representations and comparing with Galois representations in mod $p$ cohomology of Shimura curves.
K2 of Elliptic Curves over Non-Abelian Cubic and Quartic Fields
Explore K_2 of elliptic curves over non-Abelian fields, including constructions, integral elements, and numerical verification of Beilinson's conjecture. Joint work with Brunault, Hang, and Rodriguez Villegas.
Mildly Short Vectors in Ideals of Cyclotomic Fields Without Quantum Computers - MathCrypt 2022
Explore norm relations in cyclotomic fields and their applications to cryptography, focusing on finding short vectors in ideals without quantum computers.
Low Lying Zeros in Families Related to Complex Multiplication Elliptic Curves
Delve into advanced number theory concepts focusing on low-lying zeros and their relationship to CM elliptic curves, exploring mathematical patterns and theoretical frameworks in this specialized mathematical domain.
On Lehmer's Problem and Hyperbolic Geometry
Delve into the fascinating connection between Lehmer's problem and hyperbolic geometry through an advanced mathematical exploration of number theory concepts and geometric principles.
Factorizations, Elasticities and Zero-Sum Sequences
Delve into advanced number theory concepts focusing on factorizations, elasticities, and zero-sum sequences through a mathematical exploration of their properties and relationships.
The Period-Index Problem for Higher Degree Galois Cohomology Groups Over Hensel Semi-Global Fields
Delve into advanced Galois cohomology theory, exploring period-index relationships over Hensel semi-global fields and their implications for higher degree groups.
L-functions of Elliptic Curves Over Real Quadratic Fields as Special Values of Automorphic Green's Functions
Delve into advanced number theory concepts exploring L-functions of elliptic curves over real quadratic fields and their relationship to automorphic Green's functions through expert mathematical analysis.
Heuristics for the Arithmetic of Elliptic Curves and Abelian Varieties
Explore probabilistic models for elliptic curve arithmetic, examining theoretical evidence and predictions for higher-dimensional abelian varieties.
Relation Between Low-lying Zeros and Central Values
Explore the intricate relationship between low-lying zeros and central values in number theory through advanced mathematical analysis and circle method applications.