
Melissa ShermanBennett

Department of Mathematics
Harvard University

Office: 425b Science Center
Email: m_shermanbennett@berkeley.edu


Info
I'm a fifth year PhD student at UC Berkeley, currently (virtually) visiting Harvard University. I am applying for research postdocs this fall. My interests run towards cluster algebras, total positivity, and the structure of the totally nonnegative Grassmannian.
CV
Papers & Projects
 Positroid cluster structures from relabeled plabic graphs (with Chris Fraser). arXiv:2006.10247.
 1324 and 2143avoiding KazhdanLusztig immanants and kpositivity (with Sunita Chepuri). arXiv:2002.07851.
 Cluster structures in Schubert varieties in the Grassmannian (with Khrystyna Serhiyenko and Lauren Williams). Proc. Lond. Math. Soc. (6) 119 (2019) 16941744. arXiv:1902.00807 .
 Combinatorics of Xvariables in finite type cluster algebras. J. Combin. Theory Ser. A , 165 (2019), 273298. arXiv:1803.02492 .
 Large induced acyclic and outerplanar subgraphs of low treewidth planar graphs
(with Cora Borradaile and Hung Viet Le). Graphs and Combinatorics (2017), 33, no. 6, 16211634, 2017.
arXiv:1711.00212.
 Chromatic Ramsey number of hypergraphs (with Andras Gyarfas and Alex Riasanovsky). Discrete Mathematics 340 (2017), 373378.
arXiv:1509.00551.
 On groups and their graphs. My undergraduate senior thesis, focusing on some connections between
finite groups and their Cayley graphs. Includes results on colorings of Cayley graphs that respect certain
subgroups of their automorphism groups.
Talk Slides and Notes
 Plabic graphs and cluster structures on positroid varieties, slides.
 KazhdanLusztig immanants and kpositive matrices, FPSAC 2020 "poster".
 KazhdanLusztig immanants and kpositive matrices, Berkeley Combinatorics Seminar. Notes.
 Metric properties of the affine building for SL_n, Buildings, Varieties, and Applications, MPI Leipzig. Slides
 Combinatorics of cluster structures in Schubert varieties, AMS Spring Eastern Sectional Meeting 2019, University of Connecticut. Slides
 Combinatorics of Xvariables in finite type cluster algebras, AMS Fall Central Sectional Meeting 2018, University of Michigan. Slides
Seminars
This semester I am organizing a reading group on Coxeter matroids, and coorganizing the Berkeley combinatorics seminar with Sylvie Corteel.
I coorganized the Talking About Combinatorial Objects Student Seminar (TACOS) with Mario Sanchez in Spring 2018 on Coxeter groups and related topics.
Teaching