Publications (18)
Mod gamma factors and a converse theorem for finite general linear groups
Jacksyn Bakeberg, Mathilde Gerbelli-Gauthier, Heidi Goodson +3
The local converse theorem for Rankin-Selberg gamma factors of proved by Piatetski-Shapiro over no longer holds after reduction modulo $\…
A Galois-dynamics correspondence for unicritical polynomials
Robin Zhang
In an analogy with the Galois homothety property for torsion points of abelian varieties that was used in the proof of the Mordell-Lang conjecture, we describe a correspondence bet…
Section rings of -divisors on minimal rational surfaces
Aaron Landesman, Peter Ruhm, Robin Zhang
We give bounds on the degree of generation and relations of section rings associated to arbitrary -divisors on projective spaces of all dimensions and Hirzebruch surfac…
Scalable Training of Mixture-of-Experts Models with Megatron Core
Zijie Yan, Hongxiao Bai, Xin Yao +42
Scaling Mixture-of-Experts (MoE) training introduces systems challenges absent in dense models. Because each token activates only a subset of experts, this sparsity allows total pa…
Spin canonical rings of log stacky curves
Aaron Landesman, Peter Ruhm, Robin Zhang
Consider modular forms arising from a finite-area quotient of the upper-half plane by a Fuchsian group. By the classical results of Kodaira-Spencer, this ring of modular forms may…
A positive Siegel theorem: Dynkin friezes and positive Mordell-Schinzel
Robin Zhang
We determine the number of positive integral points on -dimensional affine varieties associated to arbitrary generalized Cartan matrices. An application to the theo…
The Harris-Venkatesh conjecture for derived Hecke operators I: imaginary dihedral forms
Robin Zhang
The Harris-Venkatesh conjecture posits a relationship between the action of derived Hecke operators on weight-one modular forms and Stark units. We prove the full Harris-Venkatesh…
The Harris-Venkatesh conjecture for derived Hecke operators II: a unified Stark conjecture
Robin Zhang
We prove a compatibility theorem between the Stark conjecture and the Harris-Venkatesh conjecture for imaginary dihedral modular forms of weight . The key technical input is a g…
Corrigendum to "Modular Gelfand pairs and multiplicity-free representations"
Patrick Allen, Preston Wake, Robin Zhang
Some of the multiplicity-freeness results in ``Modular Gelfand pairs and multiplicity-free representations'' are stated in overly broad generality. We provide counterexamples and p…
Uniform bounds on periodic points of polynomials with good reduction
Isaac Rajagopal, Robin Zhang
We establish effective bounds on the number of periodic points of degree- polynomials defined over -adic fields and number fields, under a mild reduction hypothesis that…
On quadratic periodic points of quadratic polynomials
Zhiming Wang, Robin Zhang
Bounding the number of preperiodic points of quadratic polynomials with rational coefficients is one case of the Uniform Boundedness Conjecture in arithmetic dynamics. Here, we pro…
The conjecture, uniform boundedness, and dynamical systems
Robin Zhang
We survey Vojta's higher-dimensional generalizations of the conjecture and Szpiro's conjecture as well as recent developments that apply them to various problems in arithmeti…
On maximal Dynkin friezes
Robin Zhang
The maximal entries of Dynkin friezes over the positive integers have recently been determined for all finite Dynkin types except and . In this note, we explicitly const…
The Harris-Venkatesh conjecture for derived Hecke operators III: local constants
Robin Zhang
The first two papers in this series prove the Harris-Venkatesh conjecture and its refinement with the Stark conjecture for imaginary dihedral modular forms of weight . This pape…
Humanity's Last Exam
Long Phan, Alice Gatti, Ziwen Han +1144
Benchmarks are important tools for tracking the rapid advancements in large language model (LLM) capabilities. However, benchmarks are not keeping pace in difficulty: LLMs now achi…
Modular Gelfand pairs and multiplicity-free representations
Robin Zhang
We give a generalization of Gelfand's criterion on the commutativity of Hecke algebras for Gelfand pairs and multiplicity-free triples over algebraically closed fields of arbitrary…
Towards the -adic derived Hecke algebra for weight one forms
Robin Zhang
This note outlines an approach to defining -adic Shimura classes and -adic derived Hecke operators on the completed cohomology of modular curves from upcoming work by the aut…
Grupos ortogonales sobre cuerpos de caracterÃstica positiva
Robin Zhang
This exposition examines the theory of orthogonal groups and their subgroups over fields of positive characteristic, which has recently been used as an important tool in the study…