# Daniel Kriz

## Princeton University

I graduated in 2018 from Princeton University.

My advisers were Christopher Skinner and Shouwu Zhang. I have now moved to MIT. Previously, I was also an undergraduate at Princeton.
In the Fall of 2016, I visited the I.H.E.S..

## Mathematical Interests

I am interested in algebraic number theory, particularly in arithmetic geometry. Most recently I have been studying special value congruences of p-adic L-functions and their relation to Heegner points and cycles. Previously, I have also done work in geometric topology regarding the Heegaard-Floer and Khovanov homologies of knot theory.

## Research

Here are some of my recent papers.

A New p-adic Maass-Shimura operator and supersingular Rankin-Selberg p-adic L-functions.

Prime twists of elliptic curves (with Chao Li), to appear in *Mathematical Research Letters*.

Heegner points at Eisenstein primes and twists of elliptic curves (with Chao Li), submitted.

Congruences between Heegner points and quadratic twists of elliptic curves (with Chao Li), submitted.

A Galois cohomological proof of Gross's factorization theorem, submitted.

Generalized Heegner cycles at Eisenstein primes and the Katz p-adic L-function, *Algebra and Number Theory* vol. 10, no 2, 2016, pp. 309-374. Arxiv (minor differences from the published version)

On a conjecture concerning the maximal cross number of unique factorization indexed sequences, appeared in *J. Number Theory*, vol 133, 9 (September 2013), 3033-3056. This paper is a result of the research I did as a participant in the Duluth REU, run by Professor Joe Gallian at the University of Minnesota Duluth.

A spanning tree cohomology theory for links (with Igor Kriz), appeared in *Advances in Mathematics*, vol 255, 1 (April 2014), 414-454. Arxiv

Field theories, stable homotopy theory, and Khovanov homology (with Po Hu, Igor Kriz), *Topology Proceedings*, vol 48, 2016, pp. 327-360. Arxiv

## Expository

Here is an introductory article to Étale cohomology, written for the final project of my algebraic geometry class with Nick Katz in Spring 2012.

An Excursion into Étale Cohomology.

### Email

dkriz@princeton.edu
This page last modified on November 30, 2018.