**I am an Assistant Professor in the Department of Mathematics and Statistics at Smith College.**

My work is primarily
in **combinatorial optimization and approximation algorithms** (my PhD was in **Operations Research**, under David Shmoys at Cornell). I am particularly interested
in **stochastic optimization problems in graphs:** how
well can spatial decisions be made when only
probabilistic information is available?

The ** graph/network setting** becomes even more intriguing as a growing number of scientists (ecological, social) have adopted this tool to **model complex heterogeneous connection/closeness/mixing**. These applications demand increasing awareness that both inputs and the effects of interventions may be non-deterministic. Many issues in the **sustainable management of natural resources** can be addressed from this perspective: I am particularly interested in the spread of wildfire (namely preventive controlled burning) and invasive species.

Since most combinatorial problems of interest are NP-hard we focus on **provably-good approximations** (sometimes for special cases with additional structure). I am also interested in computational exploration to understand strong qualitative departures which may occur for settings that lack convenient mathematical properties.

During 2012-2013, 2013-2014 I was a **Neukom Postdoctoral
Fellow at Dartmouth College** (at the Neukom Institute for Computational
Science) . There I sat jointly in Computer Science and Environmental Studies. During that time I first became interested in the **network-scale implications** of various models of behavior change from **behavioral economics** around voluntary provision for environmental quality. This work is joint with my postdoc advisor Richard Howarth.

**Some places I'll be Summer 2015: ** American Institute of Mathematics Workshop on Multiscale Modeling of the Food System, Mathematics of the Planet Earth 2013+ Workshop on Management of Natural Resources (hosted by DIMACS/Howard), Computational Sustainability Track (International Symposium on Mathematical Programming),
MathFest (100 Year Anniversary!)

**Summer 2016: ** I'm giving the U. Washington Trends in Optimization Seminar (May 17) , will be at the (Preparation for Industrial Careers in Mathematics workshop in late May), and I'm speaking at the July SIAM Meeting in a session on Implementing Transformational Undergraduate Modeling Experiences . In August I'll attend the Algorithms and Uncertainty Boot Camp at the Simons Institute.

**Summer 2017: ** I'm speaking at the AMS sectional Meeting at Hunter College, NYC in May, participating in the Beyond Planarity Mathematics Research Communities Workshop at Snowbird, UT in June, and will start a Geometric Combinatorics semester at MSRI (Mathematical Sciences Research Institute) in Berkeley, CA in mid August.

- G. Spencer, S. Carrattini, R.B. Howarth. ``Short-term Interventions for Long-term Change: Spreading Stable Green Norms in Networks." To appear at Review of Behavioral Economics.
- D. Rolnick. G. Spencer. ``On the Robust Hardness of Gröbner basis Computation." Journal of Pure and Applied Algebra, Volume 223, Issue 5, May 2019, Pages 2080-2100.
- G. Clark and G. Spencer. ``New bounds on the biplanar crossing number of low-dimensional hypercubes: How low can you go?" Bulletin of the Institute of Combinatorics and its Applications (BICA) 83(2018), 52-60.
- G. Spencer. "Clustered Networks Protect Cooperation Against Catastrophic Collapse." Full paper at the journal Network Science, May 2018. A poster on this work was presented at "Complex Networks 2017" in Lyon, France.
- Y. Wei, G. Spencer. "Measuring the value of accurate link prediction for network seeding." Computational Social Networks, 2017, 4:1.
- G. Spencer.``Sticky Seeding in Discrete-Time Reversible-Threshold Networks." Discrete Mathematics and Theoretical Computer Science (DMTCS) Vol. 18:3, 2016, 2.
- J. De Loera, S. Margulies, M. Pernpeintner, E. Riedl, D. Rolnick, G. Spencer, D. Stasi, J. Swenson ``Graph-coloring ideals: Nullstellensatz certificates, Gröbner bases for chordal graphs, and hardness of Gröbner bases." Proceedings of the International Symposium on Symbolic and Algebraic Computation (ISSAC) 2015.
- D. Shmoys, G. Spencer. Extended Journal Version: "Approximation algorithms for fragmenting a graph against a stochastically-located threat." Theory of Computing Systems 56(1), January 2015, p 96-134.
- G. Spencer. "Robust Cuts Over Time: Combatting the Spread of Invasive Species with Unreliable Biological Control." AAAI Proceedings, 2012.
- D.B. Shmoys, G. Spencer. “Approximation algorithms for fragmenting a graph against a stochastically-located threat.” To appear, WAOA Proceedings 2011. Invited to Special Issue of the journal Theory of Computing Systems.
- I. Gorodezsky, R. Kleinberg, D.B. Shmoys, G. Spencer. “Improved lower bounds for the universal and a priori TSP.” APPROX-Random Proceedings 2010, pp. 178-191.
- G. Spencer, F. Su. “The LSB Theorem Implies the KKM Lemma.” The American Mathematical Monthly, 114:2 (February 2007).

- J. Asplund, E. Czabarka, G. Clark, G. Cochran, A. Hamm, G. Spencer, L. Szekely, L. Taylor, Z. Wang. ``Using Block Designs in Crossing Number Bounds.'' Under Revision.
- T. Liu. G. Spencer. ``Biased Edge-Weighting Schemes Can Boost Reproducibility of Centrality Measures in Brain Networks." Submitted.
- E. Mainou, G. Spencer, D. Shepardson, R. Dorit. ``The wisdom of a crowd of near-best fits: Drug-Resistant Tuberculosis in the United States." Submitted.
- "Optimizing Exam Scheduling at Cornell University." An upcoming draft on consulting work for the Registrar's Office with David Shmoys and Bob Bland.
- My undergraduate math thesis at Harvey Mudd: "Combinatorial Consequences of Relatives of the Lusternik-Schnirelmann-Borsuk Theorem."
- Available online, unfinished: G. Spencer, F. Su. "Using Topological Methods to Force Maximal Complete Bipartite Subgraphs Of Kneser Graphs."

**Graph Theory, MTH 255 (Smith College).
** Spring 2018 (28 students) and Spring 2016 (22 students). Course builds from immediate implications of definitions and classic existence results to careful analysis of graph algorithms. Proof-based lectures paralleled by a series of MATLAB-based labs that develop key questions in modern network science (degree distribution, degrees of separation, etc). Supplementing traditional exams, students conduct team-based final project to extend a topic from class (mathematical or computational). Main project deliverable is a class presentation.
Sample computational labs: Lab 3: Random Walk Visit Frequency and Preferential Attachment, Lab 4: Max Cut: Random and Greedy Partitions, Local Improvement.

**Optimization (as MTH 353 at Smith College, and CS 84/184 at Dartmouth College). ** Spring 2017 (22 students), Spring 2015 (14 students), Winter 2013 (23 students). Senior/Seminar/Master's-level. Linear Programming with Duality, Integer Programming and Modeling, Dynamic Programming, Specialized Methods. Course included weekly homeworks, bi-weekly computational lab (AMPL), prelim, final, final project. Sample computational labs: Lab 3: Facility Location and Amazon Locker Placement, Lab 4: Smoothing Inpatient Load in Hospitals.

**Discrete Mathematics, MTH 153 (Smith College).
** Nine sections during Fall 2014-Spring 2018 (32-38 students per section).
Combinatorics (including Discrete Probability), Number Theory, and Graph Theory. Develops several proof techniques (including: induction, contradiction, combinatorial proofs). Weekly homeworks, "Proof Lab" days culminate in revise-and-resubmit Proof Portfolio, midterm and final.
A "letter to colleagues" about the Proof Portfolio appears in the April/May 2017 Issue of the MAA Focus Magazine (pages 10-13).

**Modeling in the Sciences, MTH/CSC 205 (Smith College).
** Spring 2016 (20 students). Sustainability-themed series of modules on Markov Models (age-structure and compartment models, randomness, notions of convergence), LP/IP (spatial processes and planning), Dynamic Programming (planning over time). Technical Lectures, short worksheets, extended computational labs (in MATLAB), contemporary literature review with discussion (15+ research papers over the semester), and final project with primary research-literature sources and presentation. Similar to Dartmouth Course listed below.

**Computational Toolbox for Environmental Sustainability, ENVS 80.4 (Dartmouth College).
** Winter 2014 (9 students). Zero-technical prerequisite course for junior/senior Environmental Studies majors. Markov Models, LP/IP, Dynamic Programming. Technical Lectures, short worksheets, extended computational labs (MATLAB), contemporary literature review with discussion, final exam, and final project. A short "letter to colleagues" about this course appeared in the August/September 2015 Issue of the MAA Focus Magazine (pages 35-37).