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.