Sarah Day. B.S. with Highest Honors (Mathematics/Physics) Emory University, Spring 1998

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1 Sarah Day Department of Mathematics Jones Hall 123 College of William and Mary (757) P.O.Box 8795 Williamsburg, VA sday/ RESEARCH INTERESTS Dynamical Systems Theory with an emphasis on topological and numerical methods, Computational Topology, and applications to Biology, Medicine, Materials Science, and Physics ACADEMIC TRAINING Ph.D. (Mathematics) Georgia Institute of Technology, Summer 2003 A Rigorous Numerical Method in Infinite Dimensions, Ph.D. dissertation advisor: Dr. Konstantin Mischaikow M.S. (Mathematics) Emory University, Spring 1998 Chaotic Dynamics on Julia Sets for the Quadratic Family, M.S. dissertation advisor: Dr. Steven Batterson B.S. with Highest Honors (Mathematics/Physics) Emory University, Spring 1998 ACADEMIC POSITIONS Associate Professor of Mathematics, College of William and Mary, 2011-present Long Term Visitor, Institute for Mathematics and its Applications (IMA), January-May 2014 Assistant Professor of Mathematics, College of William and Mary, Postdoctoral Fellow, MSRI, Fall 2006 VIGRE Assistant Professor of Mathematics, Cornell University, Visiting Researcher, Vrije Universiteit Amsterdam, PEER-REFEREED PUBLICATIONS 14. C. King, K. Shipman, S. Day, and M. D. LaMar, Dimension and mortality in linear stage class models of Acartia tonsa, Proceedings of the Sixth International Symposium on Biomathematics and Ecology Education and Research, S. Day and W. D. Kalies, Rigorous Computation of the Global Dynamics of Integrodifference Equations with Smooth Nonlinearities, SIAM J. Numer. Anal. 51, no. 6, , 2013.

2 S. Day J. B. van den Berg, S. Day, and R. Vandervorst, Braided Connecting Orbits in Parabolic Equations via Computational Homology, J. Diff. Eq., 255(6): , doi: /j.jde , M. Fujiwara, G. Pfeiffer, M. Boggess, S. Day, and J. Walton, Coexistence of competing stagestructured populations, Sci. Rep. 1, doi: /srep00107, S. Day, W. D. Kalies, and T. Wanner, Verified Homology Computations for Nodal Domains, Multiscale Model. Simul. 7(4): , S. Day, R. Frongillo, and R. Treviño, Algorithms for Rigorous Entropy Bounds and Symbolic Dynamics, SIAM J. Appl. Dyn. Syst. 7(4), , S. Day, H. Kokubu, S. Luzzatto, K. Mischaikow, H. Oka, and P. Pilarczyk, Quantitative Hyperbolicity Estimates in One-Dimensional Dynamics, Nonlinearity 21, , S. Day, W. D. Kalies, K. Mischaikow, and T. Wanner, Probabilistic and Numerical Validation of Homology Computations for Nodal Domains, Electron. Res. Announc. Amer. Math. Soc. 13:60 73, S. Day, J. P. Lessard, and K. Mischaikow, Validated Continuation for Equilibria of PDEs, SIAM J. Numer. Anal. 45, , S. Day, Y. Hiraoka, K. Mischaikow, and T. Ogawa, Rigorous Numerics for Global Dynamics: a study of the Swift-Hohenberg equation, SIAM J. Appl. Dyn. Syst. 4, 1 31, S. Day, O. Junge, and K. Mischaikow, Towards Automated Chaos Verification, EQUADIFF 2003, World Scientific, Singapore, , S. Day, O. Junge, and K. Mischaikow, A Rigorous Numerical Method for the Global Analysis of Infinite Dimensional Discrete Dynamical Systems, SIAM J. Appl. Dyn. Syst. 3, , S. Day, Towards a Rigorous Numerical Study of the Kot-Schaffer Model, Dynam. Systems Appl. 12, 87 97, S. Day, B. Grivna, E. McCartney, and E. Silva, Power Weakly Mixing Infinite Transformations, New York J. Math. 5, 17 24, AWARDS 2014 Plumeri Award, College of William & Mary 2013 Simon Teaching Prize, Mathematics Department, College of William & Mary 2012 Evans-Hall Lectureship Award, Emory University 2011 WM Alumni Fellowship Award for Excellence in Teaching

3 S. Day 3 FUNDING Principal Investigator on CAREER: Computational Dynamics and Topology. NSF DMS ($472,000), Principal Investigator on Dynamics at a Fixed Resolution. NSF DMS ($128,281), (with one year extension). Co-Principal Investigator on the group grant CSUMS: Theory, Techniques, and Research in Computational Mathematics. NSF DMS ($668,775), (with one year extension). PROFESSIONAL ACTIVITIES Co-Organizer for the Workshop on Algebraic Topology in Dynamics, Differential Equations, and Experimental Data, IMA, February Department Hiring Committee , William and Mary Faculty Assembly (FAC, COPAR, and FUPC committees) , Fall 2013, (Chair of FAC) Department Personnel Committee , IMA Hiring Committee William and Mary Women in Science and Engineering (WISE) Advisory Council Lecturer (one of three) for the TopMath Summer School on Topology, Dynamics, and Computation, Technische Universität München, August PME/Math Club Advisor and Co-organizer CSUMS lecture series/special topics courses and Freshman and Major Advisor Department Undergraduate Curriculum Committee Member, , , and Co-organizer for GMU-WM Workshop on Undergraduate Research in Computational Mathematics, George Mason University, April 2008 and April Department Merit Evaluation Committee Member, , and AWM (Association for Women in Mathematics) Mentor, 2007 SIAM Conference on Applications of Dynamical Systems, Snowbird Referee for Journal of Mathematical Biology, Physica D, SIAM Journal on Numerical Analysis, SIAM Journal on Applied Dynamical Systems, SIAM Journal on Scientific Computing, IWOTA.

4 S. Day 4 TEACHING EXPERIENCE Assistant/Associate Professor, College of William and Mary: Calculus I and II for the Life Sciences, Differential Equations I and II, Introduction to Mathematical Biology, Topology, Topics in Computational Mathematics, Senior Seminars on Computational Homology, Dynamics, Mathematical Models, and Mathematical Biology, Honors Research, Nonlinear Dynamics, Reading Groups on Algebraic Topology and Computational Dynamics VIGRE Assistant Professor, Cornell University: Differential Equations and Dynamical Systems, Computational Homology Graduate Instructor, Georgia Institute of Technology: Calculus 1, 2, Survey of Calculus, Differential Equations MENTORING postdocs: Jesse Berwald , Yu-Min Chung 2014-present. graduate student: Allison Proffer, Masters in Applied Science, undergraduate research students: current students: Eric Berry (Mathematics, co-adviser Y-M Chung) 2014-, Martin Salgado- Flores (Mathematics, co-advisers J. Berwald, Y-M Chung) 2013-, Katherine Shipman (Biology, co-adviser M. D. LaMar) William and Mary honors students (year project completed): Kassie Archer (2009), Allison Corish (co-adviser M. D. LaMar, 2012), David Gould (2009), Ryan Gryder (co-adviser M. D. LaMar, 2014), Benjamin Holman (2011), Catherine King (co-adviser M. D. LaMar, 2014), Brian Paljug (2009), Georgia Pfeiffer (2011), Niha Zubair (2009) summer research students: Claire Bobst (WM 2013, co-adviser J. Berwald) Adam Chacon (Cornell 2006), Jakub Gedeon (WM 2012, co-adviser J. Berwald), Chris Green (Cornell 2006), Rafael Frongillo (Cornell 2006), Yanni Lai (WM 2012), Philipp Meerkamp (Cornell 2006), Kelly Spendlove (WM 2012, co-adviser J. Berwald), Rodrigo Trevino (Cornell 2006), Michael Trotta (WM 2012, co-adviser J. Berwald) SELECTED PRESENTATIONS (since 2006) Symbolic Dynamics and Entropy via Conley Index Theory. PIMS, UBC, May Tools from Computational Topology with Applications in Medicine and the Life Sciences. University of Florida Colloquium, February Outer Approximation and Dynamics via Conley Index Theory. IMA Workshop, University of Minnesota, February Discontinuity and Global Dynamics of Pulse-Coupled Oscillators. Hale Memorial Conference on Dynamics of Differential Equations, Georgia Tech, March 2013.

5 S. Day 5 Population Dynamics via Computational Topology. VCU Mathematical Biology Seminar, September Capturing Butterfly Effects. Emory University, May Automated Index Processing for Symbolic Dynamics and Entropy Bounds. IV Developers Workshop on the Conley-Morse Database Project, Kauai, March Quantifying Patterns in a Coupled-Patch Population Model. Joint Mathematical Meetings, Session on Computational and Applied Topology, Boston, January Dynamics and Tools from Topology. Computational Cell Biology program, Cold Spring Harbor Laboratory, Long Island, July Validated Continuation: a study of the Swift-Hohenberg Equation. AMS 2010 Fall Southeastern Section Meeting, Session on Differential Equations and Applications to Physics and Biology, Richmond, November Computational dynamics and tools from topology. William and Mary department colloquium, September Quantifying patterns in a coupled-patch population model. AMS 2010 Spring Eastern Section Meeting, Session on Topological and Computational Dynamics, Newark, May Computational dynamics and tools from topology. Oliver Club (colloquium) talk, Cornell University, April Computational topology in the study of discrete dynamical systems. Computation Topology Seminar, IAS, November Computer-assisted proofs for dynamical systems. Applied Mathematics Seminar, George Washington University, October Computer-assisted proofs for dynamical systems. Joint CSUMS seminar talk with Rafael Frongillo, William and Mary, September Braids and connecting orbits in parabolic PDEs. William and Mary department colloquium, September Connecting orbits for parabolic PDEs via braid theory. Workshop on Computational Topology and Dynamics, MSU, Bozeman, August Symbolic dynamics via computational topology. Workshop on Computational Algebraic Topology, MFO (Oberwolfach), June/July Constructing symbolic dynamics representations via Conley Index theory. FoCM 2008, Hong Kong, June Computer-assisted proofs for the Kot-Schaffer model. AMS Spring Southeastern Sectional Meeting, Session on Mathematical Modeling in Biology, Baton Rouge, March Real Henon Maps Entropy. CANDY 08, Imperial College London, March 2008.

6 S. Day 6 Computer-assisted proofs for dynamical systems. George Mason University, February Algorithms for symbolic dynamics and entropy bounds. ICIAM 07, Zurich, July Validated continuation. SIAM Conference on Applications of Dynamical Systems, Snowbird, May/June Computer-assisted proofs in dynamical systems. colloquium, Wichita State University, April Computational tools for measuring topological entropy. AMS 2007 Spring Southeastern Sectional Meeting, Session on Dynamical Systems, Davidson, March Computing symbolic dynamics and entropy for nonlinear systems. Rutgers University, November Dynamics I, II, and III. seminar series, MSRI, September Computational topology in the study of dynamical systems. Workshop on Applications of Topology in Science and Engineering, MSRI, September Topological methods for dynamical systems. mini-course, Workshop on Recent Developments in Arrangements and Configuration Spaces, MSRI, August Validity of homology computations for nodal domains. Invited talk, Workshop on computational and topological aspects of dynamics, Leiden, May Chaotic Dynamics: a first example and beyond. Math Club talk. College of William and Mary, February Computer-assisted proofs for dynamical systems. College of William and Mary, February Computer-Assisted Proofs for Dynamical Systems: from stationary solutions to global attractors. Florida Atlantic University, February Continuation and Computer-Assisted Proofs: a study of the Swift-Hohenberg system. Vrije Universiteit, Amsterdam, January CONFERENCES AND WORKSHOPS (since 2006) Rigorously Verified Computing for Infinite Dimensional Nonlinear Dynamics Workshop, BIRS, September Combinatorial/Topological Frameworks for Multiparameter Nonlinear Dynamics, Lorentz Center, Leiden, August Algebraic Topology - Methods, Computation and Science 6 Conference, PIMS, May Workshop on Topology in Dynamics, Differential Equations and Data, IMA, February Workshop on Rigorous Computation for Infinite Dimensional Nonlinear Dynamics. AIM, Palo Alto, August Hale Memorial Conference on Dynamics of Differential Equations, Georgia Tech, March 2013.

7 S. Day 7 IV Developers Workshop on the Conley-Morse Database Project, Kauai, March Joint Mathematics Meetings, January 2012 (Boston), January 2010 (San Francisco) and January 2009 (Washington, DC.). AMS 2010 Fall Southeastern Section Meeting, Session on Differential Equations and Applications to Physics and Biology, Richmond, November AMS 2010 Spring Eastern Section Meeting, Session on Topological and Computational Dynamics. Newark, May Computational Topology and Dynamics Workshop, MSU, Bozeman, August Workshop on Rhythms in the Hypothalamus and Pituitary. AIM, Palo Alto, August Workshop on Computational Algebraic Topology, MFO Oberwolfach June/July FoCM 2008, Workshop on Computational Dynamics, Hong Kong, June AMS 2008 Spring Southeastern Sectional Meeting, Session on Mathematical Modeling in Biology, Baton Rouge, March Computer-Assisted Nonlinear Dynamics (CANDY 08). Imperial College London, March Spring Topology and Dynamics Conference (STDC 08). Milwaukee, March ICIAM 07. Zurich, July SIAM Conference on Applications of Dynamical Systems. Snowbird, May/June AMS 2007 Spring Southeastern Sectional Meeting, Session on Dynamical Systems. Davidson, March Workshop on Computational Applications of Algebraic Topology. semester workshop at MSRI, Fall Workshop on computational and topological aspects of dynamics. Lorentz Center, Leiden, May 2006.