The K-moduli space of a family of conic bundle threefolds, with L. Ji, P. Kennedy-Hunt, M. Quek, submitted.
Rational unicuspidal plane curves of low degree, with N. Singh, submitted.
Moduli of boundary polarized Calabi-Yau pairs, with K. Ascher, D. Bejleri, H. Blum, G. Inchiostro, Y. Liu, and X. Wang, submitted.
Smooth limits of plane curves of prime degree and Markov numbers, with D. Stapleton, Journal de l'Ecole Polytechnique.
K-stability and birational models of moduli of quartic K3 surfaces, with K. Ascher and Y. Liu, Inventiones Mathematicae.
K-moduli of curves on a quadric surface, with K. Ascher and Y. Liu, Journal of the Institute of Mathematics of Jussieu.
Wall crossing for K-moduli spaces of plane curves, with K. Ascher and Y. Liu, Proceedings of the London Mathematical Society.
Maximal Chow constant and cohomologically constant fibrations, with D. Stapleton, Communications in Contemporary Mathematics.
Moduli of surfaces in P3, Compositio Mathematica.
Hyperbolicity and uniformity of varieties of log general type, with K. Ascher and A. Turchet, International Math Research Notices.
Moduli of higher dimensional varieties, with exercises, with D. Bejleri, in preparation.
This is a book for graduate students to learn the K-moduli theory of Fano varieties and the KSB-moduli theory of canonically polarized varieties, with the necessary tools to do research in this area. It contains many exercises and is intended to be accessible to students with a background in algebraic geometry at the level of Hartshorne. A draft is available on request, but the K-moduli chapter can be found on the next line.
An introduction to K-moduli, with exercises.
These notes on K-moduli grew out of notes written for the 2022 AGNES Summer School on moduli of varieties and are meant to be accessible to graduate students with at least a first course in algebraic geometry.
GAeL summer school notes on Introduction to moduli of varieties.
These notes were written for the 2024 GAEL Summer School in Torino, Italy. They intend to serve as an introduction to several aspects of moduli of varieties: the minimal model program and singularities, moduli of canonically polarized varieties, moduli of Fano varieties, and wall-crossing in moduli of varieties.
AGGITATE summer school notes on Wall crossing in moduli of varieties.
These notes were written for the 2024 AGGITATE LMS Summer School at the University of Essex. They intend to serve as an introduction to one perspective on wall-crossing in moduli of varieties. These lectures happened simultaneously with courses on GIT, K-stability, and stacks and good moduli spaces, so are not entirely self-contained.
An introduction to the minimal model program, slides from a general audience talk at the Fields Institute Symposium in honor of Caucher Birkar. This talk was for the general public, and the slides were intended to be accessible to anyone who knows what a polynomial is. The video recording is here, including a panel discussion with after the talk. (My talk starts about 24 minutes in.)
Advice for the virtual job market, Early Career section of the AMS Notices September 2021 Issue
This is a reflection of my experience on the job market over Zoom, with broadly applicable advice for early career mathematicians on the market.
Reflections on the Covid job market, with R. Palak Bakshi, Mathematical Association of America Math Values Blog
This is an honest summary of my thoughts and experiences on the job market in 2020-2021.
How to have Lunch in the Time of Covid, with A. Kobin, Early Career section of the AMS Notices January 2021 Issue
This is an account of our regular 'Lunch in the Time of Covid' meetings, panels that highlighted issues relevant to early career mathematicians in the wake of the pandemic and beyond.
Actionable advice for early career mathematicians on the academic job market, Early Career section of the AMS Notices November 2020 Issue
This is an article aimed at early career mathematicians trying to find balance between their present job stage and responsibilities, future career prospects and success on the job market, and experiencing the weight of a global pandemic.