12 papers
The integral -ring of the stack of smooth hyperelliptic curves
Michael Ruofan Zeng
We compute the integral -ring of the moduli stack of smooth hyperelliptic curves of genus over a field of characteristic zero. We show that it is a free…
Tensor-generating line bundles on toric varieties
Daigo Ito, Michael R. Zeng, Xiangru Zeng
A line bundle is -generating if its powers generate the derived category of perfect complexes. Refining the derived Nakai--Moishezon criterion of Ito--Olander, we characte…
On Intersections of System Normalizers
Ting Gong, Yuan Lu, Yong Yang +1
We give a negative answer to Problem 17.39 of the Kourovka Notebook. For every odd prime power and every , we construct a finite metabelian group with $Z_\inf…
Total 3-closure for projective special linear groups
Ting Gong, Yong Yang, Michael Ruofan Zeng
A finite group is totally -closed if every faithful permutation representation of it is -closed. We study this property for the finite simple projective special linear groups…
Alternating Groups and Embeddings into Groups Invariably Generated by Two Prime-Order Elements
Ting Gong, Yong Yang, Michael Ruofan Zeng
For any distinct primes and , we prove that there is a finite group which does not embed into any finite group invariably generated by an element of order and an element…
Albilich: Steerable Proof-State Orchestration for LLM-Based Mathematical Research with CAS Integration
Ting Gong, Michael Ruofan Zeng, Yong Yang
Large language models can contribute useful ideas to mathematical research, yet long-horizon proof attempts remain difficult to coordinate, evaluate, and reproduce. We present Albi…
FactorLibrary: From Polynomials to Circuits via Recursive Subgoals
Rohan Pandey, Michael Ruofan Zeng, Weikun K. Zhang +5
Finding minimal arithmetic circuits for polynomials over finite fields is a combinatorially hard problem central to algebraic complexity theory. We formulate it as a reinforcement…
Oriented Cohomology Rings of Some Moduli Spaces via Blowups
Arkamouli Debnath, Michael Ruofan Zeng
Oriented cohomology theories provide a general framework to perform intersection-theory-type calculus. The Chow ring, algebraic -theory, and Levine--Morel's algebraic cobordism…
CircuitBuilder: From Polynomials to Circuits via Reinforcement Learning
Weikun K. Zhang, Rohan Pandey, Bhaumik Mehta +5
Motivated by auto-proof generation and Valiant's VP vs. VNP conjecture, we study the problem of discovering efficient arithmetic circuits to compute polynomials, using addition and…
The Grothendieck Group of the Variety of Spanning Line Configurations
Michael Ruofan Zeng
We study the Grothendieck group of the variety of spanning line configurations introduced by Pawlowski--Rhoades [arXiv:1711.08301] as a geometric model for the generalize…
-Mackey functors in Macaulay2
Thomas Brazelton, David Chan, Benjamin Mudrak +5
We introduce the CpMackeyFunctors package for Macaulay2, which allows for computations with Mackey functors over a cyclic group of prime order.
Brackets and Projective Geometry in Macaulay2
Dalton Bidleman, Timothy Duff, Jack Kendrick +1
We introduce the Brackets package for the computer algebra system Macaulay2, which provides convenient syntax for computations involving the classical invariants of the special lin…