# PhD-Thesis

*Symmetry Reduction in Convex Optimization with Applications in Combinatorics*. Under supervision of Etienne de Klerk and Monique Laurent.

PDF.

# Publications

## Preprints

**Daniel Brosch**and**Sven Polak**, New lower bounds on crossing numbers of K(m,n) from permutation modules and semidefinite programming, arXiv, 2022.

## Published

**Daniel Brosch**and**Etienne de Klerk**, Jordan symmetry reduction for conic optimization over the doubly nonnegative cone: theory and software, Optimization Methods and Software 2021.*Optimization Methods and Software, arXiv*.**Daniel Brosch**,**Monique Laurent**and**Andries Steenkamp**, Optimizing Hypergraph-Based Polynomials Modeling Job-Occupancy in Queuing with Redundancy Scheduling, SIAM Journal on Optimization 2021.*SIAM Journal on Optimization, arXiv*.**Daniel Brosch**and**Etienne de Klerk**, Minimum energy configurations on a toric lattice as a quadratic assignment problem, Discrete Optimization 2020.*Discrete Optimization, arXiv (extended results)*.

## Others

**Master's Thesis**:*Semidefinite Bounds for Unequal Error Protection Codes*. Under supervision of Frank Vallentin.

PDF.

# Talks

## Planned

## Past

Europt 2023, Budapest, August 2023,

**The flag algebra of rooted binary trees.**

slidesOberwolfach workshop: Mixed-integer Nonlinear Optimization: A Hatchery for Modern Mathematics, Oberwolfach, August 2023,

**Is the set of trees convex?**

slidesSIAM AG23, Eindhoven, July 2023,

**Möbius Transform Based Bounds for Constant Weight Codes.**

slidesSIAM OP23, Seattle, May-June 2023,

**Flag Sums of Squares for Sidorenko's Conjecture.**

slidesMAAG 2023, Georgia Tech, April 2023,

**The Flag Algebra of Rooted Binary Trees.**

slides.Georgia Tech Graph Theory & Combinatorics Seminar, Georgia Tech, April 2023,

**New lower bounds on crossing numbers of $K_{m,n}$.**

slides.Semidefinite optimization approaches to classical and quantum combinatorial optimization, Cologne University, February 2023,

**SDPs for Extremal Combinatorics.**

slides.Three days of computational methods for extremal discrete geometry, Cologne University, December 2022,

**New lower bounds on crossing numbers of $K_{m,n}$.**

slides.University of Klagenfurt, October 2022,

**Derivatives in Continuous Combinatorics.**

slides.ICCOPT 2022, Lehigh University, July 2022,

**Moebius-Transform Based Symmetry Reduction for Optimization in Binary Variables**.

slides.Workshop on Conic Linear Optimization for Computer-Assisted Proofs, Oberwolfach, 12.4.2022,

**The Symmetries of Flag-Algebras**.

slides.Discrete Math Seminar, University of Massachusetts Amherst, 1.4.2022,

**Symmetry reduced Flag-hierarchies**.

slides.*Polynomial optimization reading group (CWI, Amsterdam)*, March 2022,**Symmetry reduced Flag-hierarchies.**SIAM AG21, August 2021, and

SIAM OP21, July 2021:

**More efficient and flexible Flag-Algebras coming from polynomial optimization**.

slides.Virtual OR Seminar, Tilburg University, February 2021:

**More efficient and flexible Flag-Algebras**.Oberseminar "Reelle Geometrie und Algebra", Uni Konstanz, January 2021:

**More efficient and flexible Flag-Algebras**.*Shared seminar CWI reading group*/Cologne Oberseminar, January 2021:**More efficient and flexible Flag-Algebras**.*Polynomial optimization reading group (CWI, Amsterdam)*, February and March 2020.:**A two-part introduction to symmetry reduction for SDPs**.6th International Conference on Continuous Optimization (ICCOPT), August 2019:

**Minimum energy configurations on a toric lattice as a quadratic assignment problem**.

slides.

A more detailed CV is available here.

**Co-authors:** Etienne de Klerk, Monique Laurent, Sven Polak, Andries Steenkamp.