3. Postdoctoral Program - MSRI

Other mathematical breakthroughs that occurred during the program include: Collin-Ghiggini-
Honda and Kutluhan-Lee-Taubes‟s proof that “Embedded contact homology” (and, hence, by
earlier work of Hutchings and Taubes, Seiberg-Witten homology) is isomorphic to Heegaard-
Floer homology; the development of bordered Floer homology, an invariant for parametrized
surfaces and three-manifolds with parameterized boundary, which can be used to compute
Heegaard Floer homology for (closed) three-manifolds; categorification of quantum groups and
their representations (Khovanov-Lauda, Rouquier, Webster) and Webster‟s categorification of
Reshetikhin-Turaev tangle invariants; and Grigsby-Wehrli‟s discovery of a relation between
sutured Floer homology and Khovanov homology.
Program 4: Complementary Program 2009-10 (CP)
August 17, 2009 to May 21, 2010
MSRI had a small Complementary Program comprised of two postdoctoral fellows (Christopher
Hillar and Christopher Severs), one research professor, four research members, one graduate
student, and four guests.
Christopher Hillar completed his second year as a postdoctoral fellow at MSRI. In 2009–10, he
was a member of the Complementary Program for the fall semester and the External Postdoctoral
Program for the spring semester. In the fall semester, Hillar‟s work was divided into two
sections: Pure Mathematics and Theoretical Neuroscience.
In Pure Mathematics, Hillar finished up a large-scale computational project on the Secant
Conjecture in Schubert calculus, proved the independent set conjecture in algebraic statistics
using some infinite dimensional Groebner basis tools he had developed with Aschenbrenner, and
studied the stabilization problems in toric algebra. In Neuroscience, Christopher Hillar
developed a course with his mentor, Dr. Sommer, on neurologically plausible circuitry for
clustering and memory.
Christopher Severs completed his Ph.D. at Arizona State University prior to joining MSRI‟s
Complementary Program in 2009–10. Although he was not directly part of the Tropical
Geometry Program, he was interested in this subject and participated in the activities of this
program. At the same time, with Deputy Director Helene Barcelo and Ph.D. student Jacob
White, he co-authored and submitted a journal article to the Transactions of the American
Mathematical Society that was subsequently accepted for publication.
Severs also colaborated with fellow MSRI member, John Shareshian, from the Complementary
Program and Einar Steingrimsson from the UC Berkeley. Though they had not submitted any
papers, the collaboration with Steingrimsson led Severs to his next postdoctoral fellowship at
Reykjavik University in Iceland.
1.4 Postdoctoral Program supported by the NSF supplemental grant DMS-
0936277
In the Spring of 2009, MSRI (together with all the other NSF-funded mathematical institutions)
proposed and received funds (DMS-0936277) for additional postdoctoral fellowships. This
funding supported the research of talented junior future professors and leading research who
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