Doctor of Philosophy in Homogeneous Dynamics and Trace Formula
Supervisor: Prof. Dr. Alexander Gorodnik.
Online resume
Zhiyuan Deng
PhD student in mathematics
Doctoral student at the Zurich Graduate School of Mathematics, working around homogeneous dynamics, trace formulae, representation theory, and the Langlands program.
Education
Master of Fundamental Mathematics
Focused on representation theory and the Langlands program. Full scholarship supported by the Archimedes Institute.
Bachelor of Science in Mathematics and Applied Mathematics
Received an Individual Sports Scholarship in Dec 2018.
Skills
Homogeneous dynamicsTrace formulaeRepresentation theoryLanglands programAutomorphic formsL-functionsTheta correspondenceNumber theoryAlgebraic geometryArithmetic geometryErgodic theoryDynamical systemsDifferential equationsMathematical writingLaTeX
Research
Homogeneous dynamics and trace formula
- Current doctoral research at the Zurich Graduate School of Mathematics.
- Works around homogeneous dynamics, trace formulae, representation theory, and related number-theoretic structures.
The equivalence of Godement-Jacquet and Langlands-Jacquet L-functions
- Recollected the classical theory of L-functions by Riemann, Hecke, and Tate.
- Studied equivalences between two types of L-functions via theta correspondence.
- Studied spherical varieties toward a unitary equivalence of L-functions.
Local Langlands Programme
- Studied Langlands theory and presented the Local Langlands Conjecture for GL(2) in a seminar.
- Worked through modular forms and analytic number theory with graduate students at Shandong University.
- Discussed early chapters of texts by Bushnell-Henniart and Bump.
The classification of polygons with genus 2 and 3
- Completed an arithmetic geometry course with grade A- and ranked 6th among 65 classmates.
- Finished a thesis exploring refinements to existing classification methods.
- Strengthened foundations in algebra and number theory through an international conference setting.
Hopf bifurcation analysis in a diffusive SIP model with time delay
- Analyzed stability of SIP/SIR models and interpreted related biological phenomena.
- Presented ordinary differential equations and geometric theory in the research group seminar.
- Completed mathematical writing and thesis work with LaTeX.
TA / RA
P-adic number seminar
Dynamical systems and ergodic theory
Local Langlands Correspondence on GL(2)
Ordinary Differential Equations and Geometric Theory
Selected schools
- Satellite conference in number theory of the International Congress of Basic Science
- School and workshop: Ergodic Theory and Parabolic Dynamics, Warsaw IMPAN and MIMUW
- Relative Trace Formulae master class, University of Copenhagen
- Suzhou University summer school on Theta Correspondence
- Arizona Winter Semester 2021: Virtual School in Number Theory
- AGITTOC Foundations of Algebraic Geometry, Stanford University, Ravi Vakil
- AASU Algebra and Arithmetic Summer School, University of Antwerp
- Smooth Representations of Reductive P-adic Groups over Arbitrary Fields, Peking University
- Algebraic Geometry, Algebraic Number Theory, Representation Theory Summer School, University of Chinese Academy of Sciences
- The Road to Mathematics: Algebra and Number Theory Summer School, HIT