Faculty

Institution

Unit

Venue

Peter Humphries

Assistant Professor

University of Virginia

Affiliations

College and Graduate School of Arts and Sciences

Department of Mathematics

Peter Humphries is currently serving as a College And Graduate School Of Arts And Sciences Assistant Professor at University of Virginia.

Honors

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Experiences

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Education

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Peter Humphries

University of Virginia

Assistant Professor

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mathematics mathematical sciences number theory analytic number theory applied mathematics algebraic number theory modular forms spectral theory asymptotic analysis automorphic forms representation theory mathematical physics algebraic geometry geometry of numbers pure mathematics combinatorial theory physics mathematical analysis nonlinear phenomena finite fields statistical physics statistical mechanics geometric topology analytic combinatorics mertens conjecture test vectors hoheisel phenomenon theoretical physics function spaces nonlinear science polyhedron quantum chaos symmetry (physics) phase retrieval stochastic geometry discrete geometry generalized functions unified field theory foundation of mathematics formal theory theoretical mathematics asymptotic formula diophantine analysis elliptic function mathematical chemistry lower bounds harmonic space complex geometry global analysis nonlinear functional analysis function theory sieve theory standard zero-free region standard zero-free maass form maass eigenforms maass forms pólyaʼs conjecture weighted sums liouville function random wave conjecture dihedral maaß forms hybrid subconvexity fourth moment identity

Notable Scholarly Works

Notable Federal Grants

Collaborators

Lp$L^P$‐Norm Bounds for Automorphic Forms via Spectral Reciprocity. Proceedings of the London Mathematical Society (2025)

Peter HumphriesRizwanur Khan

applied mathematicspure mathematicsanalytic number theorynumber theoryspectral reciprocitymathematicsautomorphic formsspectral theory

New Variants of Arithmetic Quantum Ergodicity. Communications in Mathematical Physics (2025)

Peter HumphriesJesse Thorner

mathematical physicsalgebraic number theoryapplied mathematicsergodic theorymathematical sciencesanalytic number theoryhecke-maass cusp formsnew variantsmodular formsnumber theorymathematicsarithmetic quantum ergodicityautomorphic formsspectral theoryquantum mechanics

Sparse Equidistribution of Geometric Invariants of Real Quadratic Fields. Journal of the European Mathematical Society (2025)

Peter HumphriesAsbjørn Christian Nordentoft

geometry of numberssparse equidistributionapplied mathematicscomplex geometrygeometrygeometric group theorysmall subgroupsgeometric topologymodular formsmathematicshyperbolic orbifoldsgeometry and topologymathematical sciences

Archimedean Newform Theory For. Journal of the Institute of Mathematics of Jussieu (2024)

Peter Humphries

formal theorytheoretical mathematicsalgebraic number theorygeometry of numbersapplied mathematicspure mathematicsgroup theoryanalytic number theorycombinatorial theorymathematicsfoundation of mathematicsrepresentation theoryspectral theoryalgebraic geometrymathematical sciences

Zeros of Rankin–Selberg L -Functions in Families. Compositio Mathematica (2024)

Peter HumphriesJesse Thorner

hybrid-aspect subconvexity boundalgebraic number theoryasymptotic analysisapplied mathematicsfunctional analysismathematical analysisanalytic number theorydensity estimatemodular formsnumber theoryeffective multiplicity onemathematicsrepresentation theoryautomorphic formsspectral theorymathematical sciences

Test Vectors for Archimedean Period Integrals. Publicacions Matemàtiques (2023)

Peter HumphriesYeongseong Jo

archimedean period integralstest vectors

The Newform K-Type and P-Adic Spherical Harmonics. Israel Journal of Mathematics (2023)

Peter Humphries

harmonic analysisgeometric analysisnewform k-typemathematicsharmonic spacemathematical sciences

The Twelfth Moment of Hecke L-Functions in the Weight Aspect. Mathematische Annalen (2023)

Peter HumphriesRizwanur Khan

twelfth momentmathematical physicshecke l-functionsweight aspectmathematical chemistrymathematicsmathematical sciences

Optimal Small Scale Equidistribution of Lattice Points on the Sphere, Heegner Points, and Closed Geodesics. Communications on Pure and Applied Mathematics (2022)

Peter HumphriesMaksym Radziwiłł

asymptotic analysisgeometry of numbersapplied mathematicsgeometric analysisstatistical physicsgeometrylattice pointsanalytic number theorystochastic geometrystatistical mechanicsdiscrete geometrynumber theorymathematicssmall ballsheegner pointsgeometry and topologymathematical sciences

Distributing Points on the Torus via Modular Inverses. The Quarterly Journal of Mathematics (2021)

Peter Humphries

various statisticssmall-scale equidistributionasymptotic analysisalgebraic number theoryapplied mathematicsgeometry of numberssparse equidistributionanalytic number theorycombinatorial theorynumber theorymodular formsmathematicsalgebraic geometrymathematical sciences

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Peter Humphries

Assistant Professor

University of Virginia

Affiliations

College and Graduate School of Arts and Sciences

Department of Mathematics

Peter Humphries is currently serving as a College And Graduate School Of Arts And Sciences Assistant Professor at University of Virginia.

Honors

Create free account to unlock more features

Experiences

Create free account to unlock more features

Education

Create free account to unlock more features

Peter Humphries

University of Virginia

Assistant Professor

You can click a keyword to filter the displayed items

Notable Scholarly Works

Notable Federal Grants

Collaborators

Lp$L^P$‐Norm Bounds for Automorphic Forms via Spectral Reciprocity. Proceedings of the London Mathematical Society (2025)

Peter HumphriesRizwanur Khan

applied mathematicspure mathematicsanalytic number theorynumber theoryspectral reciprocitymathematicsautomorphic formsspectral theory

New Variants of Arithmetic Quantum Ergodicity. Communications in Mathematical Physics (2025)

Peter HumphriesJesse Thorner

Sparse Equidistribution of Geometric Invariants of Real Quadratic Fields. Journal of the European Mathematical Society (2025)

Peter HumphriesAsbjørn Christian Nordentoft

Archimedean Newform Theory For. Journal of the Institute of Mathematics of Jussieu (2024)

Peter Humphries

Zeros of Rankin–Selberg L -Functions in Families. Compositio Mathematica (2024)

Peter HumphriesJesse Thorner

Test Vectors for Archimedean Period Integrals. Publicacions Matemàtiques (2023)

Peter HumphriesYeongseong Jo

archimedean period integralstest vectors

The Newform K-Type and P-Adic Spherical Harmonics. Israel Journal of Mathematics (2023)

Peter Humphries

harmonic analysisgeometric analysisnewform k-typemathematicsharmonic spacemathematical sciences

The Twelfth Moment of Hecke L-Functions in the Weight Aspect. Mathematische Annalen (2023)

Peter HumphriesRizwanur Khan

twelfth momentmathematical physicshecke l-functionsweight aspectmathematical chemistrymathematicsmathematical sciences

Optimal Small Scale Equidistribution of Lattice Points on the Sphere, Heegner Points, and Closed Geodesics. Communications on Pure and Applied Mathematics (2022)

Peter HumphriesMaksym Radziwiłł

Distributing Points on the Torus via Modular Inverses. The Quarterly Journal of Mathematics (2021)

Peter Humphries

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2
3
4
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Institution

Cornell University

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Institution

Cornell University

automorphic forms

theoretical mathematics

David J Zywina

Institution

Cornell University

diophantine analysis

algebraic number theory

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number theory

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Scott Ahlgren

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mock modular form

modular form

Yuval Flicker

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Ohio State University

algebra

mathematical science

Ken Ono

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mathematics

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Giacomo Micheli

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