# Number Theory & Algebraic Geometry

Number theory is one of the most ancient and fundamental branches of mathematics. Originally it was mainly occupied with finding natural solutions of algebraic equations. For example, solving the equation x^2+y^2=z^2 describes all right-angle triangles with integral side lengths. Nowadays, number theory is very diverse and relates to nearly all other areas: algebra and algebraic geometry, group representation theory, analysis, including complex and non-archimedean ones, dynamics and probability, model theory. Main directions represented in our group are: representation theory, modular forms, automorphic forms and L-functions, algebraic geometry, p-adic methods and non-archimedean methods.

Faculty members in Number Theory & Algebraic Geometry:

• Ehud de Shalit: p-adic uniformization, p-adic properties of Shimura varieties and modular forms, p-adic representations of reductive groups over local fields.
• Shai Evra: Graph theory, Number theory, Representation theory.
• Hershel Farkas (emeritus): Complex function theory, Riemann surfaces, Theta functions, Combinatorial number theory.
• David Kazhdan (emeritus): Representation theory, combinatorics
• Elon Lindenstrauss: Ergodic theory, Dynamical systems, and their applications to number theory.
• Ron Livne: Algebraic geometry, Modular forms, Diophantine equations.
• Jasmin Matz: Automorphic forms, Trace formula, Analytic number theory.
• Zev Rosengarten: Number theory, Algebraic geometry.
• Tomer Schlank: Arithmetic geometry, Algebraic topology.
• Ari Shnidman: Arithmetic geometry, Arithmetic statistics, Automorphic forms.
• Michael Temkin: Algebraic geometry and non-archimedean geometry, birational geometry, resolution of singularities, valued fields.
• Yaakov Varshavski: Algebraic and arithmetic geometry, Algebraic groups, Geometric aspects of Langlands's program.
• Shaul Zemel: Modular and Automorphic Forms, Weil Representations, Theta Lifts, Thomae Formulae, Lattices.
• Tamar Ziegler: Ergodic theory, Number theory, Combinatorics.