7 papers
Positive Toeplitz operators on pluriharmonic Fock space: Schatten class criteria and sharp norm comparisons
Sam Looi
Let be a positive Borel measure on $\C^n$. For every , we prove that the Toeplitz operator induced by on pluriharmonic Fock space belongs to…
When the Berezin transform fails to detect compactness: Toeplitz operators with symbols on weighted Bergman spaces
Sam Looi
For every and , we construct whose Toeplitz form extends to a bounded, noncompact operator on the weighted Bergman spaces $A^2_γ(\mathbb…
Learning to Coordinate Symbolic Tools: LLM Agents for Verified Sum-of-Squares Certificates
Bohan Chen, Shivam N. Patel, Richard Hoffmann +2
Tool calling allows large language models (LLMs) to invoke external computation during problem solving, a useful capability in various fields including AI for mathematics. We study…
Human agency in initial human-AI proof formalization workflows
Katherine M. Collins, Simon Frieder, Jonas Bayer +14
For centuries, human mathematicians have written proofs to substantiate their mathematical arguments; yet, the ability to automatically verify the validity of proofs has long been…
Positive Berezin liminf does not imply essential positivity for radial Toeplitz operators on Bergman and Fock spaces
Sam Looi
We study whether essential positivity \[ Ï_{\mathrm{ess}}(T_f)\subset [0,\infty) \] of a radial Toeplitz operator on Bergman and Fock spaces can be detected from the asymptotic be…
A counterexample to the Berger--Coburn conjecture
Sam Looi
Berger and Coburn proposed an endpoint boundedness criterion for Toeplitz operators on the Bargmann--Fock space in which the decisive quantity is the heat transform of the symbol a…