This volume highlights the mathematical research presented at the 2019 Association for Women in Mathematics (AWM) Research Symposium held at Rice University, April 6-7, 2019. The symposium showcased research from women across the mathematical sciences working in academia, government, and industry, as well as featured women across the career spectrum: undergraduates, graduate students, postdocs, and professionals.

The book is divided into eight parts, opening with a plenary talk and followed by a combination of research paper contributions and survey papers in the different areas of mathematics represented at the symposium:

• algebraic combinatorics and graph theory
• algebraic biology
• commutative algebra
• analysis, probability, and PDEs
• topology
• applied mathematics
• mathematics education

Presents cutting-edge research, which disseminates knowledge and facilitates awareness of novel advances by members of the math community Features research by women mathematicians, which counteracts the gender imbalance and impostor syndrome particularly present in STEM fields Contains research across various disciplines, raising awareness among the contributors and their audience of the high-level work carried out by women mathematicians in virtually every field of mathematics

Inhalt
Preface.- I. From the Plenary Talks.- Finite element methods for elliptic distributed optimal control problems with pointwise state constraints (S.C. Brenner).- II. Algebraic Combinatorics and Graph Theory.- Some q-exponential formulas involving the double lowering operator for a tridiagonal pair (S. Bockting-Conrad).- Distance graphs generated by five primes (D.D-F. Liu, G. Robinson, A. Chavez).- Combinatorial characterization of queer supercrystals (M. Gillespie, G. Hawkes, W. Poh, A. Schilling).- (Tenner).- III. Algebraic Biology.- From chaos to permanence using control theory (S. Koshy-Chenthittayil, E. Dimitrova).- Classification on large networks (A. Haupt, T. Schultz, M. Kharami, N. Tran).- Gröbner bases of convex neural code ideals (K. Phillipson, E.S. Dimitrova, M. Honecker, J. Hu, Q. Liang).- Gröbner bases of convex neural code ideals (B. Stigler, A. Zhang).- IV. Commutative Algebra.- Depth of powers of squarefree monomial ideals (L. Fouli, H.T. Hà, S. Morey).- A note on the uniqueness of zero-divisor graphs with loops (A. Li, R. Miller, R.P. Tucci).- Some combinatorial cases of the three matrix analog of Gerstenhaber's theorem (J. Rajchgot, M. Satriano, W. Shen).- Structure of semigroup rings (H. Srinivasan).- Using Monte Carlo particle methods to estimate and quantify uncertainty in periodic parameters (A. Arnold).- A note on singularity formation for nonlocal transport equation (V. Hoang, M. Radosz).- Prescribing initial values for the sticky particle system (R. Hynd).- Towards directed collapsibility (R. Belton, R. Brooks, S. Ebli, L. Fajstrup, B.T. Fasy, C. Ray, N. Sanderson, E. Vidaurre).- Contact Open Books and Sympectic Lefschetz Fibrations (B. Acu).- A robust preconditioner for high-contrast problems (Y. Gorb, D. Kurzanova, Y. Kuznetsov).- On the dimension reduction in prestrained elasticity (S. Jimezes Bolanos).- Machine learning in crowd flow exit data (F.P. Medina).- The matter of shape (M. Ozkar).- Being research-based and research-minded in helping K-12 mathematics education (A. Ekmekci, A. Papakonstantinou).- The Rice University school mathematics project (A. Papakonstantinou, A. Ekmekci).