Alexander Engström Miller Research Fellow Department of Mathematics University of California, Berkeley 851 Evans Hall #3840 Berkeley, CA 94720-3840 USA Research Interests Algebraic Statistics, Discrete Geometry, Commutative Algebra, Topological Combinatorics. PhD thesis My advisor was Svante Linusson and co-advisor Jakob Jonsson. The thesis, Topological Combinatorics, was defended May 8, 2009 at KTH and the opponent was Günter M. Ziegler.

Students

Patrik Norén did his Master thesis on algebraic statistics and graph homomorphism ideals. He is now a PhD student at KTH. Erik Sjöland did his Bachelor thesis on Ramsey theory.

Preprints

9.

Random Ideals, with O. Andersson Forsman, in preparation 2009.

8.

Generalized Plunnecke and BSG theorems, in preparation 2009.

7.

Codimension-one toric fiber products, with S. Sullivant, in preparation 2009.

6.

Cohomological Ramsey theory, preprint 2008.

5.

Cellular resolutions from polyhedral subdivisions, with A. Dochtermann, preprint 2008.

4.

Cut ideals of K4-minor free graphs are generated by quadrics, preprint 2008, 8 pp.

3.

Tverberg graphs, preprint 2008, 8 pp.

2.

A new subgraph counting identity, preprint 2007, 16 pp.

1.

Transitive graphs in counterexamples of Karp's conjecture, preprint 2005, 20 pp.

Papers

10.

Betti numbers of edge ideals via combinatorial topology, with A. Dochtermann, Electron. J. Combin. 16 (2009), no. 2, 24 pp.

9.

Upper bounds on the Witten index for supersymmetric lattice models by discrete Morse theory, European J. Combin., 30 (2009), no. 2, 429-438.

8.

Discrete Morse functions from Fourier transforms, Experiment. Math., 18 (2009), no. 1, 45-53.

7.

Inequalities on Well-Distributed Point Sets on Circles, JIPAM. J. Inequal. Pure Appl. Math. 8 (2007), no. 2, Article 34, 5 pp.

6.

Set partition complexes, Discrete Comput. Geom. 40 (2008), no. 3, 357-364.

5.

The g-theorem matrices are totally nonnegative, with M. Björklund, J. Combin. Theory Ser. A. 116 (2009), no. 3, 730-732.

The g-theorem matrices are totally nonnegative (extended abstract), Oberwolfach Rep. 4 (2007), no. 1. European Mathematical Society (EMS), Zurich, pp. 217-219.

4.

Independence complexes of claw-free graphs, European J. Combin. 29 (2008), no. 1, 234-241.

3.

Complexes of Directed Trees and Independence Complexes, Discrete Math. 309 (2009), no. 10, 3299-3309.

2.

A short proof of a conjecture on the connectivity of graph coloring complexes, Proc. Amer. Math. Soc. 134 (2006), no. 12, 3703-3705.

1.

A Note on Two Multicolor Ramsey Numbers, Electron. J. Combin. 12 (2005), 1, 3 pp.

Papers in Mathematics Education

1.

Noviser och experter löser problem (in Swedish), with A. Sola, Nämnaren 35 (2008), no.1, 51-55.