Juan Muñoz-Echániz

I am a Research Assistant Professor (postdoc) at the Simons Center for Geometry and Physics at Stony Brook University, mentored by Simon Donaldson. I received my PhD in 2023 at Columbia University, advised by Francesco Lin. My CV.

Email: jmunozechaniz-at-scgp.stonybrook.edu

I am on the academic job market this year.

I am interested in gauge theory, Floer homology, and their applications to low-dimensional topology. In my recent work, I study the interplay between gauge theory, mapping class groups of 4-manifolds and complex singularities.

Papers

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, arXiv preprint
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, arXiv preprint

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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