John M. Holmes Curriculum Vitae Department of Mathematics Phone: (716)

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1 John M. Holmes Curriculum Vitae Phone: (716) Math Tower; 231 West 18th Ave, Website: johnholmesmath.wordpress.com Columbus OH, EMPLOYMENT Ross Assistant Professor 2015 Present University of Notre Dame Teaching Assistant University of Notre Dame EDUCATION Ph.D. in Mathematics. Advisor: Dr. A. Alexandrou Himonas, May 2015 Thesis: The Cauchy Problem for Several Nonlinear Evolution Equations M.S. in Mathematics. May 2013 M.S. in Applied Mathematics (Financial Economics). August 2010 Wabash College B.A., Mathematics and Economics. May 2009 RESEARCH INTERESTS Functional and harmonic analysis for nonlinear partial differential equations. Local well-posedness and asymptotic behavior of solutions to partial differential equations. Existence of solutions to randomly forced partial differential equations. Diffusion equations and their applications in financial mathematics and stochastic differential equations. PUBLICATIONS 1. T. Cosimano, A. Himonas, and J. Holmes, Optimal Investing and Consumption under Early Resolution of Uncertainty and Incomplete Markets, in preparation. 2. J. Holmes, The Cauchy problem for the Benjamin-Bona-Mahoney equation, in preparation. 3. J. Holmes and F. Tiglay, The Cauchy problem for the Hunter-Saxton equation in Besov spaces, submitted. 4. J. Holmes, B. Keyfitz and F. Tiglay, Nonuniform dependence on initial data for compressible gas dynamics: The Cauchy problem on R 2, SIAM Journal on Mathematical Analysis, (2017, to appear). 5. J. Holmes and F. Tiglay, Continuity properties of the solution map for the Euler-Poisson equation, Journal of Mathematical Fluid Mechanics, (2017, to appear). 6. J. Holmes and R. Thompson, Well-posedness and continuity properties of the Fornberg-Whitham equation in Besov spaces, Journal of Differential Equations, 263, 2017,

2 John Holmes 2 7. J. Holmes, Well posedness and regularity of the generalized Burgers equation in periodic Gevrey spaces, Journal of Mathematical Analysis and Applications, 454, 2017, J. Holmes and R. Thompson, Classical solutions of the generalized Camassa-Holm equation, Advances in Differential Equations, 22, 2016, J. Holmes, Well posedness of the Fornberg-Whitham equation on the circle, Journal of Differential Equations, 260, 2016, J. Holmes, Continuity properties of the data-to-solution map for the generalized Camassa-Holm equation, Journal of Mathematical Analysis and Applications. 417, 2014, A. Himonas and J. Holmes, Hölder continuity of the solution map for the Novikov equation, Journal of Mathematical Physics 54, 2013, M. Axtell, J. Stickles and W. Trampbachls Zero-divisor ideals and realizable zero-divisor graphs, Involve , J. Holmes and A. Shull, Properties of Ideal Divisors, Pi Mu Epsilon Journal, , AWARDS Best Paper Award, 9 th IMACS International Conference on Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory, Certificate for effective teaching using technology, Kaneb Center for Teaching and Learning, The Richard V. Andree Award, Pi Mu Epsilon National Mathematics Honor Society, George Lewes Mackintosh Fellowship, Distinction, Mathematics, Wabash College, Benjamin A. Rogge Memorial Award in Economics, Wabash College, George E. Carscallen Prize in Mathematics, Wabash College, Instructor TEACHING EXPERIENCE MATH 5194-B: Stochastic Calculus for Financial Mathematics II Fall 2017 I developed this course; a continuation of the spring course (below). We use the tools from stochastic calculus to price a variety of American and exotic options in continuous time. We then evaluate a number of interest rate models, and finally we introduce the mathematics necessary to understand stochastic calculus when the underlying measure is a jump diffusion process. We also learned numerical methods for solving PDEs, and implemented these methods to price exotic options. MATH 5194-A: Stochastic Calculus for Financial Mathematics I Spring 2017 I developed this graduate level course, which begins with measure theory and integration, derives Browning motion from a simple random walk, and then derives the continuous time asset pricing model of Black and Scholes. The majority of the course is spent introducing and proving the necessary background material from stochastic calculus. Since this course was never taught at Ohio State before, I developed a syllabus, day-to-day schedule and standards of evaluation for students. This was a mixed course of undergraduates and graduate students.

3 John Holmes 3 MATH 1151: Calculus 1 Spring 2017, Fall 2015, 2016, 2017 This is a first course in calculus for students at. Team taught with more than ten sections, this highly coordinated course covered topics including limits, exponential functions, derivatives and integration. My sections consistently performed at the top. MATH 3589: Introduction to Financial Mathematics Spring 2016, Fall 2016 This course introduces students to the binomial asset pricing model and the mathematical background needed to rigorously prove the results used in financial economics. MATH 10250: Elements of Calculus 1 Fall 2014 This is a first course in calculus for arts and letters, business and architect majors. Topics include limits, exponential functions, derivatives and integration. I created and maintained a website and online quiz system. MATH 10260: Elements of Calculus 2 Fall 2012 The second course in a two part series for business majors. We focused on applications of calculus ideas including constrained optimization, interest rates, and the Solow growth model. Teaching Assistant MATH 1151: Flipped and Flexible Calculus 1 Spring 2016, Fall 2015 In this half online course, student s only in person contact was a bi-weekly recitation administered by myself. We focused on collaborative learning, using worksheets and a weekly quiz to review material from the online lectures. MATH 40570/50570: Mathematical Methods in Financial Economics Spring 2014 Helped write examples and homework problems, as well as revised lecture materials which are intended to become a book. Wrote and graded homework assignments and exams, and met with students for extra help outside of class. MATH 22550: Calculus I Fall 2013 Conducted a tutorial for a first semester calculus aimed for engineering students. The tutorial focused on collaborative learning, using worksheets to guide the discussion and a weekly quiz to expose students to exam questions. I helped construct materials used by several sections, graded and held office hours. MATH 22560: Calculus II Fall 2011, Spring 2013 Conducted a tutorial where the main focus was to answer questions over homework and administer a weekly quiz and worksheet. I also constructed the materials, graded and proctored exams, and held office hours. MATH 22580: Linear Algebra/Differential Equations Spring 2012 Responsible for leading tutorials, writing and grading quizzes, holding office hours and grading exams. Tested the learning environment of a flipped classroom.

4 John Holmes 4 PRESENTATIONS The AMS Spring Central Sectional Meeting, 2018 Co-organizer of the special session on Nonlinear Evolution Equations. The AMS Fall Central Sectional Meeting University of North Texas, 2017 A note on the compressible Euler equations. The Seventh Ohio River Analysis Meeting University of Cincinnati, 2017 Continuity properties of the data to solution map for the compressible Euler equations. The Tenth IMACS International Conference on Nonlinear Evolution University of Georgia, 2017 Equations and Wave Phenomena: Computation and Theory A note on the non-periodic compressible Euler equations. 11th AIMS Conference on Dynamical Systems, Diff. Eq. and Applications Orlando Fl, 2016 The Hunter-Saxton equation in Besov Spaces on the circle. The 40th SIAM Southeastern Atlantic Section Conference University of Georgia, 2016 The periodic Cauchy problem for the Hunter-Saxton equation. Welcome Seminar, 2016 Well-posedness for three nonlinear evoluation equations. Best welcome seminar of the year! - Vitaly Bergelson PDE Seminar, 2016 A note on the Fornberg-Whitham equation. Analysis & Operator Theory Seminar, 2016 The periodic Cauchy problem for the Hunter-Saxton equation. PDE Seminar, 2015 Minimum regularity solutions for a Burgers type equation. The Ninth IMACS International Conference on Nonlinear Evolution University of Georgia, 2015 Equations and Wave Phenomena: Computation and Theory On the Cauchy problem for a Camassa-Holm type equation. Topics in Euler s Equation for Incompressible Fluids University of Notre Dame, 2014 Continuity properties of the data-to-solution map for the generalized Camassa Holm equation. 7th Workshop on Geometric Analysis of PDE and Several Complex Variables Brazil, 2013 Well posedness and regularity for a nonlinear heat equation in analytic Gevrey spaces. The Eighth IMACS International Conference on Nonlinear Evolution University of Georgia, 2013 Equations and Wave Phenomena: Computation and Theory Hölder continuity of the solution map for the Novikov equation. 70th Midwest PDE Seminar The University of Memphis, 2012 Continuity of the Data to Solution Map for the Novikov Equation in Sobolev Spaces. 9th AIMS Conference on Dynamical Systems, Diff. Eq. and Applications Orlando Fl, 2012 Well posedness of the generalized burgers equation in analytic Gevrey spaces. Math Colloquium Wabash College, 2012 Well posedness and Regularity of a Heat-Type Equation. PDE Complex Analysis and Differential Geometry Seminar The University of Notre Dame, 2012 The Initial Value Problem for a Nonlinear Heat Equation.

5 John Holmes 5 68th Midwest PDE Seminar The University of Notre Dame, 2011 Regularity Issues of the Generalized Burgers Equation. PDE Complex Analysis and Differential Geometry Seminar The University of Notre Dame, 2011 Well-posedness and regularity for the generalized Burgers equation. OTHER CONFERENCES ATTENDED 79/80th Midwest PDE Seminar University of Illinois at Chicago, th Midwest PDE Seminar University of Cincinatti, 2016 Shanks International Conference on Evolution Equations Vanderbilt University, 2016 Harmonic Analysis & Partial Differential Equations: University of Chicago, 2014 Recent Developments & Future Directions 73 Midwest PDE Seminar Northwestern University, Midwest PDE Seminar Purdue University, 2013 NSF-CBMS Regional Research Conference in the Mathematical Sciences Kansas State, Midwest PDE Seminar University of Michigan, 2013 The 5th Symposium on Analysis and PDEs Purdue University, 2012 Midwest Numerical Analysis Days 2012 The University of Notre Dame, th Midwest PDE Seminar University of Illinois at Chicago, 2012 The Seventh IMACS International Conference The University of Georgia, th Midwest PDE Seminar University of Illinois at Chicago, 2010 Fall Central AMS Section Meeting The University of Notre Dame, 2010

6 John Holmes 6 Prof. Jerry Bona Dept. of Math, Stats, and C.S. The University of Illinois at Chicago Chicago, IL bona@math.uic.edu REFERENCES Prof. Dan Boros (Teaching) lboros.9@osu.edu Prof. A. Alexandrou Himonas (Ph.D. Adviser) University of Notre Dame Notre Dame, IN himonas@nd.edu Dr. Nela Lakos (Teaching) lakos.1@osu.edu Prof. Barbara Keyfitz bkeyfitz@math.ohio-state.edu Prof. Dionyssis Mantzavinos University of Kansas Lawrence, KS mantzavinos@ku.edu.edu Prof. Feride Tiglay tiglay.1@osu.edu