3. Postdoctoral Program - MSRI

During my time at MSRI, I was also able to complete a project with Dave Anderson establishing
a connection between the geometry of arc spaces and equivariant cohomology. This work
does not involve tropical geometry, and was a focus of mine before the semester. The paper titled
‘Arc spaces and equivariant cohomology’ was placed on the arXiv and submitted in October
2009.”
Luis Felipe Tabera
PhD: University of Cantabria / University of Rennes I, 2007
“Two tools in algebraic geometry: Construction of configurations in tropical geometry and
hypercircles for the simplification of parametric curves”
Previous affiliations: University of Barcelona, Associate professor (September 2007 - December
2007); IMDEA Mathematics (Spain), Postdoctoral researcher (January 2008 - December 2008);
University of Cantabria, Postdoctoral Researcher (January 2009 - April 2009); UC Berkeley,
Postdoctoral Researcher (May 2009 - November 2009)
Professional Placement: University of Cantabria, Spain, Associate professor
Mentor at MSRI: Grisha Mikhalkin
“I have been working mainly on the notion of singular tropical hypersurfaces, trying to define
a tropical notion of singularity that is compatible with the algebraic notion via tropicalization.
I have made contact with other people interested in these notions, E. Brugallé, A. Dickenstein
and H. Markwig.
In a joint work with A. Dickenstein we have succesfully developped a theory of partial derivatives
that allow to define and compute a singular point inside a tropical hypersurface.”
Lauren Williams
PhD: MIT, 2005
“Combinatorial aspects of total positivity”
Previous affiliations: NSF postdoc at UC Berkeley (05/06),
Benjamin Peirce Asst prof at Harvard (06-09),
Viterbi Endowed postdoc at MSRI (Spring 08)
Professional Placement: UC Berkeley, assistant professor
Mentor at MSRI: Grisha Mikhalkin
While at MSRI I continued thinking about total positivity and its connections to tropical geometry.
I also investigated the connections between Teichmuller theory and tropical geometry, via
cluster algebras and cluster varieties. Gregg Musiker and I continued our work on the cluster
algebras associated to surfaces. But probably the most beneficial aspects of my postdoc at MSRI
was establishing new contacts. I had several very interesting discussions with Mark Gross about
mirror symmetry and possible connections to cluster algebras. I also met several times with my
mentor Grisha Mikhalkin, who explained to me the Thurston compactification of Teichmuller
space. And I met Rick Kenyon and had several very interesting discussions with him, which
may lead to a joint project.
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