**e-mail:** cgerig (at) berkeley (dot)
edu

**Office:** some random cafĂ©

I am currently thinking about cobordism maps in Embedded Contact Homology by counting pseudoholomorphic curves, with its relation to Seiberg-Witten theory.
My current interest is in using symplectic techniques outside of the symplectic world, in combination with gauge theory, to gain information about 4-manifolds.

My adviser is Michael Hutchings.

- Seiberg-Witten and Gromov invariants for self-dual harmonic 2-forms.
*Work in progress* - Taming the pseudoholomorphic beasts in ℝ×(S
^{1}×S^{2}).*Work in progress* - Independence of J for ECH.
*Work in progress* - Generic transversality for unbranched covers of closed pseudoholomorphic curves (with Chris Wendl). Comm. Pure Appl. Math. 2017
- Essential cohomology of the p-groups with a cyclic Subgroup of index p. Unpublished 2010

- "Riemann-Roch" for Punctured Curves. A sketch of a new proof of the Fredholm index formula for punctured pseudoholomorphic curves, which is a by-product of separate work in progress.
- Obstruction Bundle Gluing. Notes from a lecture series given by Michael Hutchings and a discussion session given by myself, at the 2015 IHES Moduli Conference.
- Solutions to "Cohomology of Groups". As an undergraduate I wrote a solutions manual to my math mentor Ken Brown's textbook.

**Math 32 - Precalculus**(Teaching Assistant). Spring 2017**Math 191 - Knot Theory**(Instructor). Spring 2016**Physics 7A - Newtonian Mechanics**(Teaching Assistant). Fall 2011, Spring 2012, Summer 2012

Syllabus. Sketched Lecture Notes. Projects.

I entered the PhD Physics program at UC Berkeley for one year, before quitting to join their math department. I worked under Dan Stamper-Kurn for a few months as a graduate student, with the intent of using cold atoms to study cQED (cavity quantum electrodynamics). I began by designing/building a laser to use in the lab and writing a documentation, Grating-Stabilized 1064nm Diode Laser, so that future students can easily build more.

For a while I ran the Graduate Social Club at UC Berkeley (a project under the graduate government), hosting small and large social events for the campus-wide graduate community.