On the Pseudonullity of Fine Selmer Groups Over Function Fields by Sohan Ghosh
Explores pseudonullity of fine Selmer groups over function fields, advancing understanding in arithmetic geometry and modular curves. Contributes to research on rational points and algebraic structures.
Uniform Versions of Shafarevich Conjecture by Plawan Das
Exploring uniform versions of Shafarevich Conjecture in arithmetic geometry, focusing on rational points on modular curves and their implications for elliptic curves and modular forms.
Rational Points on Modular Curves - Lecture 1
Explore advanced concepts in arithmetic geometry, focusing on rational points on modular curves. Gain insights into theoretical and computational aspects of this fascinating field of mathematics.
Classical and Quadratic Chabauty - Lecture 1
Explore advanced techniques for studying rational points on modular curves, focusing on classical and quadratic Chabauty methods in arithmetic geometry.
Arithmetic Field Theory for Elliptic Curves by Minhyong Kim
Explore advanced arithmetic field theory for elliptic curves, focusing on rational points on modular curves, Chabauty methods, and computational aspects in arithmetic geometry.
Counting Rational Points on Modular Curves of Genus 0 Over Number Fields by Peter Bruin
Explore techniques for counting rational points on modular curves of genus 0 over number fields, advancing understanding in arithmetic geometry and algebraic number theory.
Diophantine Stability for Elliptic Curves on Average by Anwesh Ray
Explore Diophantine stability for elliptic curves, focusing on average-case analysis. Gain insights into arithmetic geometry and modular curves through advanced theoretical and computational approaches.
A Simple Dichotomy in Serre's Uniformity Question by Davide Lombardo
Explore Serre's Uniformity Question in arithmetic geometry, focusing on rational points on modular curves and their implications for elliptic curves and number theory.
A Chabauty-Coleman-Caro-Pasten Bound in Higher Dimensions by Netan Dogra
Explore advanced techniques in arithmetic geometry, focusing on rational points on modular curves and higher-dimensional varieties using Chabauty-Coleman-Caro-Pasten methods.
Hasse Principle for Function Fields
Explore the Hasse principle's application to function fields, delving into its mathematical implications and theoretical foundations.
Moduli Spaces of Points on the Projective Line and Other Varieties with Many Symmetries
Explore equivariant birational geometry through recent results and constructions presented by Yuri Tschinkel from SCGP & NYU.
Minimal Torsion Curves in Geometric Isogeny Classes
Explore minimal torsion curves in geometric isogeny classes, delving into advanced number theory concepts and computational techniques.
Lower Bound on the Maximal Number of Rational Points on Curves over Finite Fields
Explore lower bounds on maximal rational points for curves over finite fields. Delve into strategies, Kzarnak Theory, and proofs in algebraic geometry.
Algebraic Curves with Many Rational Points over Finite Fields
Explore algebraic curves with many rational points over finite fields, focusing on maximum curves, automorphisms, and their applications in coding theory.
Probabilistic Approaches to Rational Points on Algebraic Surfaces
Explore probabilistic methods for studying rational points on algebraic surfaces, delving into advanced mathematical concepts and recent research developments.
Sparsity of Rational Points on Curves - What is Known and What is Expected
Explore the known results and open questions surrounding the sparsity of rational points on curves, gaining insights into this mathematical concept.
The Classical Circle Method - Lecture 3
Delve into advanced number theory concepts through the Classical Circle Method, exploring its applications in analytic theory and rational point counting on 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.
Systems of Many Forms with Differing Degrees
Explore advanced circle method applications in number theory, focusing on rational point counting, prime numbers, and recent developments in L-functions and Langlands program theory.