Faculty

Institution

Unit

Venue

Yuan Liu

Assistant Professor

University of Illinois Urbana-Champaign

Affiliations

College of Liberal Arts & Sciences

Department of Mathematics

Yuan Liu is currently serving as a College Of Liberal Arts & Sciences Assistant Professor at University of Illinois Urbana-Champaign.

Honors

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Experiences

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Education

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Yuan Liu

University of Illinois Urbana-Champaign

Assistant Professor

You can click a keyword to filter the displayed items

mathematics group theory mathematical sciences algebraic geometry algebraic number theory number theory algebraic theory applied mathematics algebraic topology homological algebra frattini subgroup finite fields galois cohomology restricted ramification geometric topology combinatorial theory modular forms geometry of numbers class groups analytic number theory algebraic combinatorics massey products predicted distribution inertia subgroups minimal number algebra pure mathematics rational mechanic modulus problem lower bounds commutative algebra coxeter group nilpotent groups free probability automorphic forms computational number theory enumerative geometry observability realization theory classical mechanics modular curves augmentation ideal random group free group n generators galois extension lenstra heuristics non-abelian cohen class group

Notable Scholarly Works

Notable Federal Grants

Collaborators

Presentations of Galois Groups of Maximal Extensions With Restricted Ramification. Algebra & Number Theory (2025)

Yuan Liu

algebraic theorymathematical sciencesminimal numberalgebraic combinatoricsfrattini subgroupcombinatorial theoryalgebraic number theorygalois cohomologyalgebraic topologyrestricted ramificationgroup theoryapplied mathematicsalgebraic geometrymathematics

A Predicted Distribution for Galois Groups of Maximal Unramified Extensions. Inventiones mathematicae (2024)

Yuan LiuMelanie Matchett WoodDavid Zureick-Brown

predicted distributionalgebraic number theorynumber theorygroup theorymathematics

On the Distribution of Class Groups of Abelian Extensions. arXiv (Cornell University) (2024)

Liu, Yuan

class groupgalois extensionsclass groupsfinite fieldsmodular formsnumber theorygroup theorycomputational number theorymathematics

Publisher Correction to: A Predicted Distribution for Galois Groups of Maximal Unramified Extensions. Inventiones mathematicae (2024)

Yuan LiuMelanie Matchett WoodDavid Zureick-Brown

predicted distributionpublisher correctionalgebraic number theorymaximal unramified extensionsnumber theory

Generalized Bockstein Maps and Massey Products. Forum of Mathematics Sigma (2023)

Yeuk Hay Joshua LamYuan LiuRomyar SharifiPreston WakeJiuya Wang

homological algebraalgebraic theorylower boundsmathematical sciencesfrattini subgroupgalois cohomologyalgebraic topologygroup theorymassey productsalgebraic geometrymathematicsgeometric topology

On the P -Rank of Class Groups of P -Extensions. International Mathematics Research Notices (2023)

Yuan Liu

homological algebraalgebraic theoryclass groupsmathematical sciencesfinite fieldsautomorphic formsinertia subgroupsfrattini subgroupalgebraic number theorynumber theoryrestricted ramificationgroup theorygeometry of numbersalgebraic geometrymathematics

Non-Abelian Cohen--Lenstra Heuristics in the Presence of Roots of Unity. arXiv (Cornell University) (2022)

Liu, Yuan

galois extensionhomological algebralenstra heuristicsmathematical sciencesfinite fieldsanalytic number theorymodular formsalgebraic number theorynumber theoryalgebraic topologynon-abelian cohengeometry of numbersalgebraic geometrymathematics

On the $P$-Rank of Class Groups of $P$-Extensions. arXiv (Cornell University) (2022)

Liu, Yuan

algebraic theoryclass groupsmathematical sciencesfinite fieldsanalytic number theoryinertia subgroupsalgebraic number theorynumber theoryrestricted ramificationgroup theorymathematics

Tamely Ramified Covers of the Projective Line With Alternating and Symmetric Monodromy. Algebra & Number Theory (2022)

Renee BellJeremy BooherWilliam Y. ChenYuan Liu

ramified coversmoduli spacesmathematical sciencesprojective lineenumerative geometrynumber theorygroup theorygeometry of numbersalgebraic geometrymathematics

Generalized Bockstein Maps and Massey Products. arXiv (Cornell University) (2020)

Yeuk Hay Joshua LamYuan LiuRomyar SharifiPreston WakeJiuya Wang

homological algebraalgebraic theorycommutative algebramathematical sciencesgalois cohomologyalgebraic topologygroup theorymassey productsalgebraic geometryaugmentation idealmathematicsgeometric topology

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Yuan Liu

Assistant Professor

University of Illinois Urbana-Champaign

Affiliations

College of Liberal Arts & Sciences

Department of Mathematics

Yuan Liu is currently serving as a College Of Liberal Arts & Sciences Assistant Professor at University of Illinois Urbana-Champaign.

Honors

Create free account to unlock more features

Experiences

Create free account to unlock more features

Education

Create free account to unlock more features

Yuan Liu

University of Illinois Urbana-Champaign

Assistant Professor

You can click a keyword to filter the displayed items

Notable Scholarly Works

Notable Federal Grants

Collaborators

Presentations of Galois Groups of Maximal Extensions With Restricted Ramification. Algebra & Number Theory (2025)

Yuan Liu

A Predicted Distribution for Galois Groups of Maximal Unramified Extensions. Inventiones mathematicae (2024)

Yuan LiuMelanie Matchett WoodDavid Zureick-Brown

predicted distributionalgebraic number theorynumber theorygroup theorymathematics

On the Distribution of Class Groups of Abelian Extensions. arXiv (Cornell University) (2024)

Liu, Yuan

class groupgalois extensionsclass groupsfinite fieldsmodular formsnumber theorygroup theorycomputational number theorymathematics

Publisher Correction to: A Predicted Distribution for Galois Groups of Maximal Unramified Extensions. Inventiones mathematicae (2024)

Yuan LiuMelanie Matchett WoodDavid Zureick-Brown

predicted distributionpublisher correctionalgebraic number theorymaximal unramified extensionsnumber theory

Generalized Bockstein Maps and Massey Products. Forum of Mathematics Sigma (2023)

Yeuk Hay Joshua LamYuan LiuRomyar SharifiPreston WakeJiuya Wang

homological algebraalgebraic theorylower boundsmathematical sciencesfrattini subgroupgalois cohomologyalgebraic topologygroup theorymassey productsalgebraic geometrymathematicsgeometric topology

On the P -Rank of Class Groups of P -Extensions. International Mathematics Research Notices (2023)

Yuan Liu

Non-Abelian Cohen--Lenstra Heuristics in the Presence of Roots of Unity. arXiv (Cornell University) (2022)

Liu, Yuan

On the $P$-Rank of Class Groups of $P$-Extensions. arXiv (Cornell University) (2022)

Liu, Yuan

algebraic theoryclass groupsmathematical sciencesfinite fieldsanalytic number theoryinertia subgroupsalgebraic number theorynumber theoryrestricted ramificationgroup theorymathematics

Tamely Ramified Covers of the Projective Line With Alternating and Symmetric Monodromy. Algebra & Number Theory (2022)

Renee BellJeremy BooherWilliam Y. ChenYuan Liu

ramified coversmoduli spacesmathematical sciencesprojective lineenumerative geometrynumber theorygroup theorygeometry of numbersalgebraic geometrymathematics

Generalized Bockstein Maps and Massey Products. arXiv (Cornell University) (2020)

Yeuk Hay Joshua LamYuan LiuRomyar SharifiPreston WakeJiuya Wang

1
2
10 / page

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David J Zywina

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