The Geometry and Geometric Analysis Seminar at Purdue in Fall 2026 is usually on Mondays 11:30am-12:20pm Eastern Time in MATH 731 if we meet in person. Some talks will be on zoom and the link will be included in the email announcement.
Lvzhou Chen, Mathew George, and Nicholas McCleerey are organizing this seminar in Fall 2026. If you have any questions or would like to suggest speakers, please contact one of us.
We are maintaining an email list for this seminar, through which we send notifications regarding talks and seminar lunches/dinners. You can subscribe to the list by the link here:
https://lists.purdue.edu/scripts/wa.exe?SUBED1=GEOMETRY-SEMINAR&A=1
Title: On a construction of Hermitian metrics on holomorphic vector bundles
Abstract: A fundamental construction in geometry associates with any holomorphic vector bundle E over a compact base a line bundle L (sometimes denoted O_{PE} (1)). According to a conjecture of Griffiths from the 1960s, if L admits a positively curved hermitian metric k, then E also admits a positively curved hermitian metric h. While the conjecture may be correct, we will show that it is not possible to obtain h out of k by a fiberwise construction that is functorial.
Title: H\"older estimates for Complex m-Hessian Equations
Abstract: We will discuss a simple, AI-generated, proof of the effective H\"older estimates for complex m-Hessian equations on compact K\"ahler manifolds. We will then indicate how to improve upon this to obtain effective, optimal H\"older estimates for weak solutions whose right-hand side is in L^p, with p > n/m and m > 2; this results was previously unknown even in the Monge-Amp\`ere case. Time permitting, we will also discuss the m=2 case, where the problem may be more subtle.
Title: Examples of asymptotically conical Calabi--Yau metrics with irregular tangent cones at infinity
Abstract: Using Altmann’s deformation theory of toric varieties, I will show that there are infinitely many new examples of complete Calabi–Yau metrics with irregular asymptotic cones, answering a question of Conlon and Hein. Based on a recent result of Conlon--Hein, I will also explain a combinatorial method to construct smoothable toric Calabi–Yau cones from a well-known family of rigid cones, yielding new Calabi–Yau metrics on the smoothing. This is based on a joint work with R. Conlon.