J. Andrew Newman, Ph.D.

About

I'm currently a postdoc at Carnegie Mellon University in the Department of Mathematical Sciences. My research interests are in the intersection of topology, combinatorics, and probability, in particular the study of random simplicial complexes and applying the probabilistic method to problems in topology. 

I completed my Ph.D. at The Ohio State University in 2018, and prior to my position at CMU, I was a postdoc in the Facets of Complexity research training group working in the Discrete Mathematics and Geometry group at Technische Universität Berlin from 2018 to 2020.  

Contact Information

Office: Wean Hall 7128

Office Phone: 412-268-6126

Email: anewman [at] andrew [dot] cmu [dot] edu

Research -- Preprints and Publications

• with Marta Pavelka. A conditional lower bound for the Turán number of spheres. https://arxiv.org/abs/2403.05364.

• Chromatic numbers of flag 3-spheres. https://arxiv.org/abs/2311.08499.

• with Patrick Bennett, Alan Frieze, and Wesley Pegden. On the intersecting family process. https://arxiv.org/abs/2302.09050.

• Linear embeddings of random complexes. https://arxiv.org/abs/2212.09576.

• with Florian Frick. Random complexes with free involution. https://arxiv.org/abs/2210.11316. To appear in Israel Journal of Mathematics.

• with Tom Bohman. Complexes of nearly maximum diameter. https://arxiv.org/abs/2204.11932.

• Abelian groups from random hypergraphs. Combinatorics, Probability & Computing. 2023. https://doi.org/10.1017/S0963548323000056. (also on arXiv)

• One-sided sharp thresholds for homology of random flag complexes. Journal of the LMS. 2024. https://doi.org/10.1112/jlms.12872. (also on arXiv)

• with Anton Dochtermann. Random subcomplexes and Betti numbers of random edge ideals. IMRN. 2022. https://doi.org/10.1093/imrn/rnac014. (also on arXiv)

• with Mara Belotti and Antonio Lerario. Graph invariants from the topology of rigid isotopy classes. https://arxiv.org/abs/2008.03984. To appear in Algebraic & Geometric Topology.

• Doubly random polytopes. Random Structures & Algorithms. 2021. https://doi.org/10.1002/rsa.21059. (also on arXiv)

• with Matthew Kahle. Topology and geometry of random 2-dimensional hypertrees. Discrete & Computational Geometry. 2022. https://doi.org/10.1007/s00454-021-00352-x. (also on arXiv)

• with Janko Böhm, Michael Joswig, and Lars Kastner. Random growth on a Ramanujan graph. https://arxiv.org/abs/1908.09575 

• with Francisco Criado. Randomized construction of complexes with large diameter.  Discrete & Computational Geometry. 2020. https://doi.org/10.1007/s00454-020-00248-2, (also on arXiv)

• with Davide Lofano. The worst way to collapse a simplex.  Israel Journal of Mathematics. 2021. https://doi.org/10.1007/s11856-021-2184-3. (also on arXiv)

• On the complexity of random polytopes. https://arxiv.org/abs/1904.10225.

• with Elliot Paquette. The integer homology threshold in Y_d(n, p). Proceedings of the AMS 2023. https://doi.org/10.1090/proc/16196. (also on arXiv)

• A lower bound on the number of homotopy types of simplicial complexes on n vertices. Combinatorica 2022. https://doi.org/10.1007/s00493-022-4877-6. (also on arXiv)

• Small simplicial complexes with prescribed torsion in homology. Discrete & Computational Geometry 2018. https://doi.org/10.1007/s00454-018-9987-y. (also on arXiv)

• with Matthew Kahle, Frank H. Lutz, and Kyle Parsons. Cohen--Lenstra heuristics for torsion in homology of random complexes. Experimental Mathematics 2018. (also on arXiv) https://doi.org/10.1080/10586458.2018.1473821

• Freeness of the random fundamental group.  Journal of Topology and Analysis 2018. https://doi.org/10.1142/S1793525319500468. (also on arXiv)

• with Tao Jiang. Small dense subgraphs of a graph. SIAM Journal on Discrete Mathematics 2017 31:1, 124-142. https://doi.org/10.1137/15M1007598 (also on arXiv)

Education

• Ph.D. , Mathematics. Completed July 2018. The Ohio State University.  Dissertation:  Torsion in Homology of Random Simplicial Complexes. Advisor: Prof. Matthew Kahle.

• MA, Mathematics. Completed June 2013. Miami University. Advisor: Prof. Tao Jiang.

• BA, Mathematics. Completed January 2011. Franklin College. 

Conference & Seminar Talks

• New Trends from Classical Theorems in Geometry, Topology, and Combinatorics. Casa Matemática Oaxaca. June 6, 2023.

• Special Session on Probabilistic and Extremal Combinatorics. AMS Sectional Meeting. University of Cincinnati. April 15, 2023.

• Miami University Department of Mathematics Colloquium. September 8, 2022.

• Facets of Complexity Monday Lecture. Freie Universität Berlin. May 9, 2022.

• Session on Geometric Topology. 55th Spring Topology and Dynamical Systems Conference. Baylor University. March 10th, 2022.

• Carnegie Mellon Math Club Colloquium. February 23, 2022.

• LMS workshop on applied topology. Virtual conference hosted by Queen Mary University of London. February 1, 2022. 

• Stochastic Topology Mini-Conference. Virtual conference hosted by TU Berlin. September 21, 2021.

• Algebraic Questions in Random Integral Matrices. Virtual conference hosted by Ohio State University. November 15, 2020

• Geometry and Control Seminar. SISSA. February 18, 2020.

• Combinatorics Seminar. Czech Academy of Science, Institute of Computer Science. February 12, 2020

• Applied Topology Seminar. University of Aberdeen. February 5, 2020

• Stochastic Analysis Seminar. Technische Universität Berlin. January 13, 2020

• Algebra Oberseminar. Universität Osnabrück. November 19, 2019

• Session on Random Geometry and Topology. SIAM Conference on Applied Algebraic Geometry.  Universität Bern. July 11, 2019

• Computational Topology Seminar. Technische Universität München. February 15, 2019.

• Combinatorics and Graph Theory Seminar. Freie Universität Berlin. November 28, 2018. 

• Discrete Geometry Seminar. Freie Universität Berlin. November 22, 2018. 

• Facets of Complexity Monday Lecture. Technische Universität Berlin. June 4, 2018. (Slides)

• Topology, Geometry, and Data Analysis Seminar. Ohio State University. April 10, 2018.

• Graduate Student Combinatorics Conference. University of Texas at Dallas. April 7, 2018

• Special Session on TGDA. AMS Sectional Meeting. Ohio State University. March 17, 2018.

• Combinatorics and Probability Seminar. Ohio State University. September 28, 2017.

• Stochastic Topology Seminar. ICERM. October 12, 2016.

Teaching

• Carnegie Mellon (2020 - present)

  • Spring 2024: 21-325 -- Probability

  • Fall 2023: 21-256 -- Multivariate Analysis

  • Spring 2023: 21-259 -- Calculus in Three Dimensions

  • Fall 2022: 21-325 -- Probability and 21-259 -- Calculus in Three Dimensions

  • Summer 2022: 21-325 -- Probability

  • Spring 2022: 21-325 -- Probability

  • Fall 2021: 21-259 -- Calculus in Three Dimensions

  • Spring 2021: 21-341 -- Linear Algebra

  • Fall 2020: 21-259 -- Calculus in Three Dimensions

• Ohio State (2013 - 2018)

  • Spring 2017:  Math 1152 -- Calculus II

  • Fall 2015: Math 1150 -- Precalculus

  • Spring 2015:  Math 1151 -- Calculus I

  • Fall 2014: Math 1151 -- Calculus I

• Miami University (2011 - 2013)

  • Spring 2013: Math 151 -- Calculus I

  • Fall 2012: Math 104 -- Precalculus

  • Fall 2011: Math 123 -- Precalculus