Juan Muñoz-Echániz
Juan Muñoz-Echániz
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I am an Assistant Professor at Stony Brook University, Department of Mathematics. Previously, I was a Research Assistant Professor at the Simons Center for Geometry and Physics. I received my PhD in 2023 at Columbia University, advised by Francesco Lin. My CV.
Email: juan.munoz-echaniz-at-stonybrook.edu
I am interested in gauge theory, Floer homology, and their applications to topology and geometry.
Papers
Constraints on Lefschetz fibrations with four-dimensional fibers from Seiberg--Witten theory, joint with Hokuto Konno, Jianfeng Lin and Anubhav Mukherjee, arXiv preprint
A Morse complex for the homology of vanishing cycles, joint with Aleksander Doan, arXiv preprint
Configurations of Lagrangian spheres in K3 surfaces, arXiv preprint
Counting SL(2,C) connections on Seifert-fibered spaces, Compositio Mathematica
The monodromy diffeomorphism of weighted singularities and Seiberg--Witten theory, joint with Hokuto Konno, Jianfeng Lin and Anubhav Mukherjee, arXiv preprint
On four-dimensional Dehn twists and Milnor fibrations, joint with Hokuto Konno, Jianfeng Lin and Anubhav Mukherjee, to appear in Duke Mathematical Journal
Exotic Dehn twists on sums of two contact 3-manifolds, joint with Eduardo Fernández, Geometry & Topology
A monopole invariant for families of contact structures, Advances in Mathematics
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