Resources

Here I host files which I think should be available on the web or that I like to link on my resume.

Final theses

B.Sc. Mathematics: Morse Functions and Birth-Death Bifurcations (pdf)
I prove that generic homotopies connecting Morse functions on closed manifolds are themselves Morse except at finitely many times where critical points are either born or collide (birth-death bifurcations).
M.Sc. Mathematics: Instanton Counting and qq-Characters (pdf)
The first part is a detailed and largely self-contained introduction to instanton counting, Nikita Nekrasov's procedure of computing an N = 2 gauge theory's partition function using equivariant localization. I think it is the only accessible introduction to this topic available as of yet and should be especially useful for Master's and PhD students.

The second part explains qq-characters and non-perturbative Dyson-Schwinger equations arising in instanton counting of quiver gauge theories. I think I did a good job of resolving ambiguities in Nekrasov's work, especially with regard to the role of Dynkin quiver type (ADE vs. affine). Connections to the representation theory of quantum groups and Yangians are also accessibly explained. Beware that what I present as conjectures may be regarded as resolved by experts in the field.