Carina Curto · Curriculum Vitae Department of Mathematics tel: (814) 863 9119 The Pennsylvania State University email: [email protected] 331 McAllister Building website: http://www.personal.psu.edu/cpc16/ University Park, State College, PA 16802 CV last updated: December 26, 2018 Research · Mathematical neuroscience Interests · Applied algebra, geometry, and topology · Neural networks and neural codes: theory, modeling, and data analysis Education & Employment Academic The Pennsylvania State University (PSU) State College, PA Positions Associate Professor of Mathematics Aug 2014–present Member of the Center for Neural Engineering University of Nebraska-Lincoln (UNL) Lincoln, NE Assistant Professor of Mathematics Aug 2009–Aug 2014 Courant Institute, New York University (NYU) New York, NY Courant Instructor (Mathematics) Sep 2008–Aug 2009 Rutgers, The State University of New Jersey Newark, NJ Center for Molecular and Behavioral Neuroscience May 2005–Aug 2008 Postdoctoral Associate (Neuroscience) Education Duke University Durham, NC Ph.D. in Mathematics (Algebraic Geometry & String Theory) Aug 2000–May 2005 Advisor: Prof. David R. Morrison Harvard University Cambridge, MA A.B. in Physics (Cum Laude) Sep 1996–Jun 2000 Iowa City West High School Iowa City, IA Valedictorian (4.0 GPA) Aug 1992–Jun 1996 Additional MBL Neuroinformatics Course, Woods Hole, MA Aug 2006 Education IAS Prospects in Theoretical Physics (String Theory), Princeton, NJ Jun 2002 IAS Women’s Program in Symplectic Geometry, Princeton, NJ May 2002 IAS Park City Math Institute, Park City, Utah Jul 2001 – Supersymmetry, Quantum Field Theory & Enumerative Geometry IAS Women’s Program in Mathematical Physics, Princeton, NJ May 2001 Budapest Semesters in Mathematics, Hungary Spring 1999 University of Iowa Summer French Program in Lyon, France Summer 1996 University of Iowa coursework (as a high school student, 15 courses) 1993-1996 Grants & Awards Research NIH R01 EB022862 (lead PI; $1,134,009; BRAIN Initiative grant) 2016-19 Funding – Emergent dynamics from network connectivity: a minimal model NSF DMS-1516881 (single PI; $150,000) 2015-19 – Theory of threshold-linear networks and combinatorial neural codes NSF DMS-1225666/DMS-1537228 (single PI; $164,999; transferred from UNL to PSU) 2012-16 – Memory encoding in spatially structured networks: dynamics, discrete geometry & topology 1 Sub-award from NIH R01-EY010542-19 ($33,000) 2014-15 – Regulation of photoreceptor neurotransmission (PI: Wallace Thoreson, UNMC) Janelia Visitor Program (co-PI with E. Pastalkova & V. Itskov; $61,976) 2013-15 – Development of a mathematical tool for rigorous analysis of neural activity sequences Alfred P. Sloan Research Fellowship ($50,000) 2011-15 Career Enhancement Fellowship for Junior Faculty ($31,500) 2012-13 – Woodrow Wilson National Fellowship Foundation & Andrew W. Mellon Foundation Nebraska EPSCoR First Award ($20,000) 2012-13 NSF DMS-0920845 (single PI; $109,635) 2009-13 – Stimulus representation and spontaneous activity in recurrent networks Other Statistical and Applied Mathematical Sciences Institute (SAMSI) 2016 Funding – year-long program: Challenges in Computational Neuroscience & Awards – fully funded long-term visitor (3 months) – taught a graduate course in Mathematical Neuroscience for Duke, UNC, & NC State students Institute for Mathematics and its Applications (IMA), long-term visitor 2014 – year-long program: Scientific and Engineering Applications of Algebraic Topology – fully funded long-term visitor (2.5 months) AMS Travel Award (Mathematical Congress of the Americas in Guanajuato) 2013 Named a UNL “Academic Star” 2012 UNL Visiting Scholars Grant (to support visitors) 2010, 2012 NSF S-STEM-1060322 (co-PI; $599,996; education grant) 2011-16 UNL Research Council Interdisciplinary Grant (co-PI; $5,000) 2010 NSF VIGRE Graduate Fellowship 2004–05 NSF Graduate Research Fellowship 2000–04 Duke Endowment Fellowship, Duke University 2001–04 James B. Duke Fellowship, Duke University 2000–03 University Scholars Program Fellowship, Duke University 2000–01 Mellon Mays Undergraduate Fellowship, Harvard University 1997–2000 American Physical Society Scholarship 1996–98 Detur Prize, Harvard University 1997 Varsity Letter Winner, Harvard Women’s Tennis 1996-97 Publications In progress 34. C. Curto, C. Langdon, K. Morrison. Directed cliques in threshold-linear networks. In preparation. 33. C. Langdon, K. Morrisony, C. Curtoy (yequal last authors). Combinatorial geometry of threshold-linear networks. In preparation. 32. C. Parmelee, S. Moore, K. Morrisony, C. Curtoy (yequal last authors). Predicting emergent sequences from network connectivity. In preparation. 31. K. Morrison, C. Langdon, C. Parmelee, J. Geneson, A. Degeratu, V. Itskov, C. Curto (2019). Dynamically relevant motifs in inhibition-dominated threshold-linear networks. In preparation. 30. L. Brown, C. Curto. Periodic codes and sound localization. In preparation. 29. A. Veliz-Cuba, V. Itskovy, C. Curtoy (yequal last authors). Sequences of neural activity in randomly- connected networks with Hebbian plasticity yield robust bump attractor dynamics. In preparation. Preprints/ 28. K. Morrison, A. Degeratu, V. Itskov, C. Curto. Diversity of emergent dynamics in competitive threshold- Submitted linear networks: a preliminary report. Preprint available at arXiv.org. 27. C. Curto, R. Vera. The Leray dimension of a convex code. Preprint available at arXiv.org. 26. C. Curto, N. Youngs. Neural ring homomorphisms and maps between neural codes. Submitted to Proceed- ings of the Abel Symposium, 2018. Preprint available at arXiv.org. 2 Published/ 25. C. Curto, E. Gross, J. Jeffries, K. Morrison, Z. Rosen, A. Shiu, N. Youngs. Algebraic signatures of convex Accepted and non-convex codes. Journal of Pure and Applied Algebra, in press, 2019. Preprint available at arXiv.org. 24. C. Curto, J. Geneson, K. Morrison. Fixed points of competitive threshold-linear networks. Neural Com- putation, Vol 31, pp. 94-155, 2019. 23. K. Morrison, C. Curto. Predicting neural network dynamics via graphical analysis. Book chapter in Algebraic and Combinatorial Computational Biology. R. Robeva, M. Macaulay (Eds), 2018. 22. C. Curto, A. Veliz-Cuba, N. Youngs. Analysis of combinatorial neural codes: an algebraic approach. Book chapter in Algebraic and Combinatorial Computational Biology. R. Robeva, M. Macaulay (Eds), 2018. 21. C. Curto, V. Itskov. Combinatorial neural codes. Book chapter in Handbook of Discrete and Combina- torial Mathematics, Second Edition, edited by Kenneth H. Rosen, CRC Press, 2018. 20. C. Curto, E. Gross, J. Jeffries, K. Morrison, M. Omar, Z. Rosen, A. Shiu, N. Youngs. What makes a neural code convex? SIAM J. Appl. Algebra and Geometry, vol. 1, pp. 222-238, 2017. 19. C. Curto. What can topology tells us about the neural code? Bulletin of the AMS, vol. 54, no. 1, pp. 63-78, 2017. – Also translated to Chinese for Mathematical Advances in Translation. 18. C. Curto, K. Morrison. Pattern completion in symmetric threshold-linear networks. Neural Computation, Vol 28, pp. 2825-2852, 2016. 17. W.B. Thoreson, M.J. Van Hook, C. Parmelee, C. Curto. Modeling and measurement of vesicle pools at the cone ribbon synapse: changes in release probability are solely responsible for voltage-dependent changes in release. Synapse, 70:1-14, 2016. 16. C. Giusti, E. Pastalkova, C. Curtoy, V. Itskovy (yequal last authors). Clique topology reveals intrinsic geometric structure in neural correlations. PNAS, vol. 112, no. 44, pp. 13455-13460, 2015. 15. M.J. Van Hook, C. Parmelee, M. Chen, K.M. Cork, C. Curto, W.B. Thoreson. Calmodulin enhances ribbon replenishment and shapes filtering of synaptic transmission by cone photoreceptors. Journal of General Physiology, 144:357-378, 2014. 14. C. Curto, A. Degeratu, V. Itskov. Encoding binary neural codes in networks of threshold-linear neurons. Neural Computation, Vol 25, pp. 2858-2903, 2013. 13. C. Curto, V. Itskov, A. Veliz-Cuba, N. Youngs. The neural ring: an algebraic tool for analyzing the intrinsic structure of neural codes. Bulletin of Mathematical Biology, Volume 75, Issue 9, pp. 1571-1611, 2013. 12. C. Curto, V. Itskov, K. Morrison, Z. Roth, J.L. Walker. Combinatorial neural codes from a mathematical coding theory perspective. Neural Computation, Vol 25(7), pp. 1891-1925, 2013. 11. C. Curto, D.R. Morrison. Threefold flops via matrix factorization. Journal of Algebraic Geometry, Vol 22(4), pp. 599-627, 2013. 10. C. Curto, A. Degeratu, V. Itskov. Flexible memory networks. Bulletin of Mathematical Biology, Vol. 74(3), pp. 590-614, 2012. 9. V. Itskov∗, C. Curto∗, E. Pastalkova, G. Buzsaki (*equal contribution). Cell assembly sequences arising from spike threshold adaptation keep track of time in the hippocampus. Journal of Neuroscience, Vol. 31(8), pp. 2828-2834, 2011. 8. K.D. Harris, P. Bartho, P. Chadderton, C. Curto, J. de la Rocha, L. Hollender, V. Itskov, A. Luczak, S. Marguet, A. Renart, S. Sakata. How do neurons work together? Lessons from auditory cortex. Hearing Research, Vol. 271(1-2), pp. 37-53, 2011. 7. P. Bartho, C. Curto, A. Luczak, S. Marguet, K.D. Harris. Population coding of tone stimuli in auditory cortex: dynamic rate vector analysis. European Journal of Neuroscience, Vol. 30(9), pp. 1767-1778, 2009. 3 6. C. Curto, S. Sakata, S. Marguet, V. Itskov, K.D. Harris. A simple model of cortical dynamics explains variability and state dependence of sensory responses in urethane-anesthetized auditory cortex. Journal of Neuroscience, Vol. 29(34):10600-10612, 2009. 5. C. Curto∗, V. Itskov∗ (∗equal contribution).