# Lucas Braune

I am currently an Acting Assistant Professor at the University of Washington's Department of Mathematics. Before coming to the UW, I was a Riemann Fellow at the Leibniz Universität Hannover. I obtained my PhD at IMPA, and have also spent time at the mathematics departments of the Humboldt Universität-Berlin, the University of Cambridge and PUC-Rio. You can find my CV here.

## Research

I am an algebraic geometer. My current interests include rationality questions, the minimal model program program, singularity theory (of varieties and of maps, also in positive characteristics), and moduli spaces of curves and higher dimensional varieties.

Irrational complete intersections (Preprint)
Abstract: Kollár's method for proving the irrationality of hypersurfaces extends to more general complete intersections. A complete intersection of $r$ very general hypersurfaces of degrees $d_1,\dotsc,d_r$ in complex projective $N$-space is not ruled, and therefore not rational, provided that $\sum d_i\ge \tfrac 3 4 N + 2r+1.$
Branched Covers of Cones and Kodaira Dimension (Preprint)
Abstract: In this note I compute for branched covers of cones (1) the Iitaka dimensions of their canonical divisors and (2) their Kodaira dimensions. These calculations show that among such covers there are examples in all dimensions of varieties with at most isolated quotient singularities for which the quantities (1) and (2) are distinct.

## Teaching

Current quarter:
UW, Spring 2019 - MATH 324 D Advanced Multivariable Calculus

Previous quarters:
UW, Winter 2019 - MATH 324 BC Advanced Multivariable Calculus
UW, Autumn 2018 - MATH 324 C Advanced Multivariable Calculus
UW, Spring 2018 - MATH 324 C Advanced Multivariable Calculus
UW, Winter 2018 - MATH 324 B Advanced Multivariable Calculus
UW, Autumn 2017 - MATH 308 EF Matrix Algebra with Applications
UNIRIO, Ago-Dez 2016 - Álgebra Linear 2 (in Portuguese)

## Contact

E-mail: lvhb 'at' uw.edu