This year’s contestants were Tushar Chawla’16, Weissman Mathematics; Bell Chen’17, Weissman Mathematics; Jonathan Romero’17, Zicklin Accounting; and, Gehua Zhang’17, Zicklin Mathematics. The team was prepared by Professor Jarrod Pickens, who also coached Baruch’s winning Rotman International Trading Competition in February, and by Baruch MFE student Anik Roy.

“Participating in this competition was a tremendous learning experience for our students,” said Dan Stefanica, co-director of the Master’s in Financial Engineering (MFE) program. “Preparing for the competition taught them about the algorithmic nature of the work, and being there, and winning the options market making case in competition with future traders from top schools around the country built confidence for their soon to be launched careers.”

Baruch’s team won the Options Market Making category, placed third in Cross-listed Shares Trading, and 10th in Algorithmic Sales & Trading. “Most importantly, our trading strategies had moderately high expected returns, but very low risk – we were in top eight in 8 out of 9 trading rounds in the competition,” says Stefanica.

The nation’s primary algorithmic trading competition, the UChicago Midwest Trading Competition serves as an opportunity for quantitatively driven students interested in financial markets to connect with premier financial services firms in the Chicago area.

]]>Selected answers may be viewed by clicking the section link below.

1.1 | 2.4 | 3.1 |

1.2 | 2.5 | 3.2 |

1.3 | 2.6 | 3.3 |

1.4 | 2.7 | 3.4 |

1.5 | 2.8 | 3.5 |

1.6 | 2.9 | 3.6 |

2.1 | 2.10 | 3.7 |

2.2 | 2.11 | 3.8 |

2.3 | 2.12 | 3.9 |

Department of Mathematics

Baruch College and the CUNY Graduate Center

**Contact Information:**

*Email:* elena.kosygina@baruch.cuny.edu

*Phone:* +1 (646) 312-4167

**Mailing address:**

One Bernard Baruch Way

Department of Mathematics, Box B6-230

Baruch College

New York, NY 10010

USA

**Current research interests:**

- Random walks and diffusions in random media

** Education:**

*Undergraduate:*

- Diploma in Mathematics (with Honors), 1989, Moscow State University,

Adviser: A.S. Kalashnikov. Diploma paper: “On unbounded solutions of quasi-linear degenerate parabolic equations”.

*Graduate:*

- Candidate of Science in Physics and Mathematics, 1995, Moscow State University, Department of Mathematics and Mechanics,

Adviser: A.S. Kalashnikov. Dissertation: “Cauchy problem in classes of growing functions for equations of fast diffusion type”. - Ph.D. in Mathematics, 1999, Courant Institute, New York University, Mathematics,

Adviser: S.R.S. Varadhan. Dissertation: “Behavior of relative entropy in the hydrodynamic scaling limit”. PDF

**Graduate students:**

- Omar Chakhtoun (the CUNY Graduate Center, current)

**Some papers and preprints:**

Davini, A., Kosygina, E., *Homogenization of viscous and non-viscous HJ equations: a remark and an application; Calculus of Variations and Partial Differential Equations*, 56 (2017), paper 95, 21 pages; published version*; arXiv:1608.01893v2 (*print/download is not allowed; misprints introduced by the publisher: missing commas in A(x/ε,ω) between x/ε and ω in 3 places)

Kosygina, E., Peterson, J., *Functional Limit laws for recurrent excited random walks with Markovian cookie stacks; *Electronic Journal of Probability*,* 21 (2016), paper no. 70, 24 pp.

Kosygina, E., Zerner, M. P. W., *A zero-one law for recurrence and transience of frog processes*; (in press) Probability Theory and Related Fields, 168 (2017), no. 1-2, 317–346; arXiv:1508.01953

Kosygina, E., Peterson, J., *Excited random walks with Markovian cookie stacks*; to appear in Annales de L’Institute Henri Poincare; arXiv:1504.06280

Dolgopyat, D., Kosygina, E., *Excursions and occupation times of critical excited random walks*; ALEA Lat. Am. J. Probab. Math. Stat.12 (2015), no. 1, 427–450. arXiv:1410.7090

Kosygina, E., Zerner, M. P. W., *Excursions of excited random walks on integers; * Electronic Journal of Probability, 19 (2014), article 25, 1-25.

Kosygina, E., *Crossing speeds of random walks among “sparse” or “spiky” Bernoulli potentials on integers, *Journal of Statistical Physics, 152 (2013), no. 2, 213-236; arXiv:1212.4447

Kosygina, E., Zerner, M. P. W., *Excited random walks: results, methods, open problems.* Bulletin of the Institute of Mathematics. Academia Sinica (New Series) 8 (2013), no. 1, 105-157; Published version; arXiv:1204.1895

Dolgopyat, D., Kosygina, E.,* Scaling limits of recurrent excited random walks on integers. * Electronic Communications in Probability 17 (2012), article 35, 1-14.

Kosygina, E., Mountford, T., *Crossing velocities for an annealed random walk in a random potential.* Stochastic Processes and their Applications 122 (2012), no. 1, 277–304. arXiv:1103.0515v1.

Kosygina, E., Mountford, T., *Limit laws of transient excited random walks on integers.* Annales de l’Institut Henri Poincare, Probabilites et Statistiques, 47 (2011), no. 2, 575-600. arXiv:0908.4356v2.

Kosygina, E., Mountford, T. S., Zerner, M. P. W., *Lyapunov exponents of Green’s functions for random potentials tending to zero.* Probability Theory and Related Fields, 150 (2011), no. 1-2, 43-59. arXiv:0903.4928v2.

Kosygina, E., Zerner, M. P. W., *Positively and negatively excited random walks on integers, with branching processes.* Electronic Journal of Probability, 13 (2008), paper 64, 1952-1979.

Kosygina, E., Varadhan S.R.S., *Homogenization of Hamilton-Jacobi-Bellman equations with respect to time-space shifts in a stationary ergodic medium.* Communications on Pure and Applied Mathematics, 61 (2008), no. 6, 816-847. PDF

Kosygina, E., *Homogenization of stochastic Hamilton-Jacobi equations: brief review of methods and applications.* Stochastic Analysis and Partial Differential Equations, Series of Contemporary Mathematics 429 (2007), American Mathematical Society, 189-204. PDF

Kosygina, E., Rezakhanlou, F., and Varadhan, S.R.S., *Stochastic homogenization of Hamilton-Jacobi-Bellman Equations.* Communications on Pure and Applied Mathematics, 59 (2006), no. 10, 1489-1521.PDF

Kosygina, E., *Brownian flow on a finite interval with jump boundary conditions.* Discrete and Continuous Dynamical Systems, Series B, 6 (2006), no. 4, 867-880. PDF

Kosygina, E., *On the Cauchy problem for the generalized porous medium equation.* Communications in Partial Differential Equations, 26 (2001), 841-858. PDF

Kosygina, E., *The behavior of the specific entropy in the hydrodynamic scaling limit.* The Annals of Probability, 29 (2001), no. 3, 1086-1110. PDF

Kosygina, E., *The behavior of the specific entropy in the hydrodynamic scaling limit for Ginzburg-Landau model.* Markov Processes and Related Fields, 7 (2001), no. 3, 383-417. PDF

- Collaboration Grant for Mathematicians, Simons Foundation, September 1, 2017 – August 31, 2022
- Scholar Incentive Award, Baruch College, CUNY, 2014-2015
- Simons Fellow in Mathematics, Simons Foundation, 2014-2015
- Collaboration Grant for Mathematicians, Simons Foundation, July 1, 2011 – August 31, 2016 (no cost extension until August 31, 2017)

CUNY Probability Seminar, Tuesdays, 4:15-5:15 p.m., Room 5417

Courant Institute Probability and Mathematical Physics Seminar, Fridays, 11 a.m.-12 p.m., Room 512

Columbia University Probability Seminar, Fridays, 12-1 p.m., Room 520

Baruch College of CUNY

The CUNY Graduate Center

e-mail: awapter@alum.mit.edu

**Education:**

B.S., Mathematics, M.I.T., 1975.

Ph.D., Mathematics, M.I.T., 1978.

Research Interests:

Mathematical Logic, specifically Set Theory: Large Cardinals and Forcing.

**Acknowledgement and Logic Links:**

Joel Hamkins, whom I thank for helping me to set up my initial web page, has created a page containing links of interest to logicians both in the greater New York area and elsewhere. Click here to access these links. Click here to find out information about MAMLS.

**Slides:**

Slides from my lecture “Some Results Concerning Strong Compactness and Supercompactness”, which I presented at the Winter Meeting of the ASL held January 17-18, 2003 in Baltimore, can be found by clicking here for the .dvi file, and here for the LaTeX file. Slides from my lecture “Indestructibility and Strong Compactness”, which I presented at Logic Colloquium 2003 held August 14-20, 2003 in Helsinki, Finland can be found by clicking here for the .dvi file, and here for the LaTeX file. Slides from the lecture I presented at the Baumgartner 60th Birthday Conference, held October 4-5, 2003 at Dartmouth College can be found by clicking here for the .dvi file, and here for the LaTeX file.

**Current Publication List** (last revised 9/12/15):

- “On the Least Strongly Compact Cardinal”, Israel Journal of Mathematics 35, 1980, 225-233.
- “Changing Cofinalities and Infinite Exponents”, Journal of Symbolic Logic 46, 1981, 89-95.
- “Measurability and Degrees of Strong Compactness”, Journal of Symbolic Logic 46, 1981, 180-185.
- “On a Problem of Silver”, Fundamenta Mathematicae 116, 1983, 33-38.
- “Some Results on Consecutive Large Cardinals”, Annals of Pure and Applied Logic 25, 1983, 1-17.
- “A Generalized Version of the Singular Cardinals Problem”, Fundamenta Mathematicae 121, 1984, 99-116.
- “Successors of Singular Cardinals and Measurability”, Advances in Mathematics 55, 1985, 228-241.
- “An AD-Like Model”, Journal of Symbolic Logic 50, 1985, 531-543.
- “A Cardinal Structure Theorem for an Ultrapower”, Canadian Mathematical Bulletin 28, 1985, 472-473.
- “Some Results on Consecutive Large Cardinals II: Applications of Radin Forcing”, Israel Journal of Mathematics 52, 1985, 273-292.
- (with J. Henle) “Large Cardinal Structures Below $\aleph_\omega$”, Journal of Symbolic Logic 51, 1986, 591-603.
- “On a Problem Inspired by Determinacy”, Israel Journal of Mathematics 61, 1988, 256-270.
- (with M. Gitik) “Some Results on Specker’s Problem”, Pacific Journal of Mathematics 134, 1988, 227-249.
- (with C. DiPrisco, J. Henle, and W. Zwicker) “Filter Spaces: Towards a Unified Theory of Large Cardinal and Embedding Axioms”, Annals of Pure and Applied Logic 41, 1989, 93-106.
- “Successors of Singular Cardinals and Measurability Revisited”, Journal of Symbolic Logic 55, 1990, 492-501.
- (with C. DiPrisco, J. Henle, and W. Zwicker) “Filter Spaces II: Limit Ultraproducts and Iterated Embeddings”, Acta Cientifica Venezolano 40, 1990, 311-318.
- “A Note on Strong Compactness and Supercompactness”, Bulletin of the London Mathematical Society 23, 1991, 113-115.
- (with J. Henle) “Relative Consistency Results via Strong Compactness”, Fundamenta Mathematicae 139, 1991, 133-149.
- “Some New Upper Bounds in Consistency Strength for Certain Choiceless Large Cardinal Patterns”, Archive for Mathematical Logic 31, 1992, 201-205. .dvi file, Plain TeX file.
- (with J. Henle) “On Box, Weak Box, and Strong Compactness”, Bulletin of the London Mathematical Society 24, 1992, 513-518. .dvi file, Plain TeX file.
- “On the Class of Measurable Cardinals Without the Axiom of Choice”, Israel Journal of Mathematics 79, 1992, 367-379. .dvi file, Plain TeX file.
- “On the First n Strongly Compact Cardinals”, Proceedings of the American Mathematical Society 123, 1995, 2229-2235. .dvi file, Plain TeX file.
- (with M. Magidor) “Instances of Dependent Choice and the Measurability of $\aleph_{\omega + 1}$”, Annals of Pure and Applied Logic 74, 1995, 203-219. .dvi file, Plain TeX file.
- “AD and Patterns of Singular Cardinals below $\Theta$”, Journal of Symbolic Logic 61, 1996, 225-235. .dvi file, Plain TeX file.
- “A Cardinal Pattern Inspired by AD”, Mathematical Logic Quarterly 42, 1996, 211-218. .dvi file, Plain TeX file.
- (with S. Shelah) “On the Strong Equality between Supercompactness and Strong Compactness”, Transactions of the American Mathematical Society 349, 1997, 103-128. .dvi file, Plain TeX file.
- (with S. Shelah) “Menas’ Result is Best Possible”, Transactions of the American Mathematical Society 349, 1997, 2007-2034. .dvi file, Plain TeX file.
- “More on the Least Strongly Compact Cardinal”, Mathematical Logic Quarterly 43, 1997, 427-430. .dvi file, Plain TeX file.
- “Patterns of Compact Cardinals”, Annals of Pure and Applied Logic 89, 1997, 101-115. .dvi file, Plain TeX file.
- “Laver Indestructibility and the Class of Compact Cardinals”, Journal of Symbolic Logic 63, 1998, 149-157. .dvi file, Plain TeX file.
- (with M. Gitik) “The Least Measurable can be Strongly Compact and Indestructible”, Journal of Symbolic Logic 63, 1998, 1404-1412. .dvi file, Plain TeX file.
- “Forcing the Least Measurable to Violate GCH”, Mathematical Logic Quarterly 45, 1999, 551-560. .dvi file, LaTeX file.
- “On Measurable Limits of Compact Cardinals”, Journal of Symbolic Logic 64, 1999, 1675-1688. .dvi file, Plain TeX file.
- (with J. D. Hamkins) “Universal Indestructibility”, Kobe Journal of Mathematics 16, 1999, 119-130. .dvi file, Plain TeX file.
- (with J. Henle and S. Jackson) “The Calculus of Partition Sequences, Changing Cofinalities, and a Question of Woodin”, Transactions of the American Mathematical Society 352, 2000, 969-1003. .dvi file, LaTeX file.
- (with J. Cummings) “A Global Version of a Theorem of Ben-David and Magidor”, Annals of Pure and Applied Logic 102, 2000, 199-222. .dvi file, LaTeX file.
- “A New Proof of a Theorem of Magidor”, Archive for Mathematical Logic 39, 2000, 209-211. .dvi file, Plain TeX file.
- “On a Problem of Woodin”, Archive for Mathematical Logic 39, 2000, 253-259. .dvi file, Plain TeX file.
- “Strong Compactness and a Global Version of a Theorem of Ben-David and Magidor”, Mathematical Logic Quarterly 46, 2000, 453-459. .dvi file, LaTeX file.
- (with J. Cummings) “Identity Crises and Strong Compactness”, Journal of Symbolic Logic 65, 2000, 1895-1910. .dvi file, Plain TeX file.
- “A Note on Strong Compactness and Resurrectibility”, Fundamenta Mathematicae 165, 2000, 285-290. .dvi file, LaTeX file.
- (with J. Cummings) “Identity Crises and Strong Compactness II: Strong Cardinals”, Archive for Mathematical Logic 40, 2001, 25-38. .dvi file.
- “Some Remarks on Normal Measures and Measurable Cardinals”, Mathematical Logic Quarterly 47, 2001, 35-44. .dvi file, LaTeX file.
- “Strong Compactness, Measurability, and the Class of Supercompact Cardinals”, Fundamenta Mathematicae 167, 2001, 65-78. .dvi file, LaTeX file.
- “Supercompactness and Measurable Limits of Strong Cardinals”, Journal of Symbolic Logic 66, 2001, 629-639. .dvi file, LaTeX file.
- “On the Consistency Strength of Two Choiceless Cardinal Patterns”, Notre Dame Journal of Formal Logic 40, 1999, 341-345. Note: This paper actually appeared during the summer of 2001. .dvi file, LaTeX file.
- (with M. Dzamonja) “Some Remarks on a Question of D. H. Fremlin Regarding $\epsilon$-Density”, Archive for Mathematical Logic 40, 2001, 531-540. .dvi file, LaTeX file.
- (with J. D. Hamkins) “Indestructible Weakly Compact Cardinals and the Necessity of Supercompactness for Certain Proof Schemata”, Mathematical Logic Quarterly 47, 2001, 563-571. .dvi file, LaTeX file.
- “Expanding $\kappa$’s Power Set in its Ultrapowers”, Radovi Matematicki 10, 2001, 149-156. .dvi file, LaTeX file.
- “Some Structural Results Concerning Supercompact Cardinals”, Journal of Symbolic Logic 66, 2001, 1919-1927. .dvi file, LaTeX file.
- “On Level by Level Equivalence and Inequivalence between Strong Compactness and Supercompactness”, Fundamenta Mathematicae 171, 2002, 77-92. .dvi file, LaTeX file.
- (with J. D. Hamkins) “Indestructibility and the Level-by-Level Agreement between Strong Compactness and Supercompactness”, Journal of Symbolic Logic 67, 2002, 820-840. .dvi file.
- (with J. Cummings) “Blowing up the Power Set of the Least Measurable”, Journal of Symbolic Logic 67, 2002, 915-923. .dvi file.
- “On the Non-Extendibility of Strongness and Supercompactness through Strong Compactness”, Fundamenta Mathematicae 174, 2002, 87-96. .dvi file.
- “Strong Cardinals can be Fully Laver Indestructible”, Mathematical Logic Quarterly 48, 2002, 499-507. .dvi file, LaTeX file.
- “Aspects of Strong Compactness, Measurability, and Indestructibility”, Archive for Mathematical Logic 41, 2002, 705-719. .dvi file, LaTeX file.
- “On the Level by Level Equivalence between Strong Compactness and Strongness”, Journal of the Mathematical Society of Japan 55, 2003, 47-58. .dvi file.
- (with J. D. Hamkins) “Exactly Controlling the Non-Supercompact Strongly Compact Cardinals”, Journal of Symbolic Logic 68, 2003, 669-688. .dvi file, LaTeX file.
- “Characterizing Strong Compactness via Strongness”, Mathematical Logic Quarterly 49, 2003, 375-384. .dvi file, LaTeX file.
- “Failures of GCH and the Level by Level Equivalence between Strong Compactness and Supercompactness”, Mathematical Logic Quarterly 49, 2003, 587-597. .dvi file, LaTeX file.
- “Indestructibility, Strongness, and Level by Level Equivalence”, Fundamenta Mathematicae 177, 2003, 45-54. .dvi file, LaTeX file.
- “Some Remarks on Indestructibility and Hamkins’ Lottery Preparation”, Archive for Mathematical Logic 42, 2003, 717-735. .dvi file, LaTeX file.
- “Level by Level Equivalence and Strong Compactness”, Mathematical Logic Quarterly 50, 2004, 51-64. .dvi file, LaTeX file.
- “Supercompactness and Partial Level by Level Equivalence between Strong Compactness and Strongness”, Fundamenta Mathematicae 182, 2004, 123-136. .dvi file, LaTeX file.
- (with G. Sargsyan) “Jonsson-like Partition Relations and j : V —> V”, Journal of Symbolic Logic 69, 2004, 1267-1281. .dvi file, LaTeX file.
- “Removing Laver Functions from Supercompactness Arguments”, Mathematical Logic Quarterly 51, 2005, 154-156. .dvi file, LaTeX file.
- “An Easton Theorem for Level by Level Equivalence”, Mathematical Logic Quarterly 51, 2005, 247-253. .dvi file, LaTeX file.
- “Diamond, Square, and Level by Level Equivalence”, Archive for Mathematical Logic 44, 2005, 387-395. .dvi file, LaTeX file.
- “On a Problem of Foreman and Magidor”, Archive for Mathematical Logic 44, 2005, 493-498. .dvi file, LaTeX file.
- (with G. Sargsyan) “Can A Large Cardinal Be Forced From A Condition Implying Its Negation?”, Proceedings of the American Mathematical Society 133, 2005, 3103-3108. .dvi file, LaTeX file.
- “Universal Partial Indestructibility and Strong Compactness”, Mathematical Logic Quarterly 51, 2005, 524-531. .dvi file, LaTeX file.
- “Universal Indestructibility is Consistent with Two Strongly Compact Cardinals”, Bulletin of the Polish Academy of Sciences (Mathematics) 53, 2005, 131-135. .dvi file, LaTeX file.
- (with G. Sargsyan) “Identity Crises and Strong Compactness III: Woodin Cardinals”, Archive for Mathematical Logic 45, 2006, 307-322. .dvi file, LaTeX file.
- “Indestructibility and Strong Compactness”, Proceedings of Logic Colloquium 2003, Lecture Notes in Logic 24, 2006, 27-37. .dvi file, LaTeX file.
- “How Many Normal Measures Can $\aleph_{\omega + 1}$ Carry?”, Fundamenta Mathematicae 191, 2006, 57-66. .dvi file, LaTeX file.
- “Supercompactness and Measurable Limits of Strong Cardinals II: Applications to Level by Level Equivalence”, Mathematical Logic Quarterly 52, 2006, 457-463. .dvi file, LaTeX file.
- (with P. Koepke) “The Consistency Strength of $\aleph_\omega$ and $\aleph_{\omega_1}$ being Rowbottom Cardinals without the Axiom of Choice”, Archive for Mathematical Logic 45, 2006, 721-737. .dvi file, LaTeX file.
- “Failures of SCH and Level by Level Equivalence”, Archive for Mathematical Logic 45, 2006, 831-838. .dvi file, LaTeX file.
- “The Least Strongly Compact can be the Least Strong and Indestructible”, Annals of Pure and Applied Logic 144, 2006, 33-42. .dvi file, LaTeX file.
- “Indestructibility and Level by Level Equivalence and Inequivalence”, Mathematical Logic Quarterly 53, 2007, 78-85. .dvi file, LaTeX file.
- “Supercompactness and Level by Level Equivalence are Compatible with Indestructibility for Strong Compactness”, Archive for Mathematical Logic 46, 2007, 155-163. .dvi file, LaTeX file.
- “Level by Level Equivalence and the Number of Normal Measures over $P_\kappa(\lambda)$”, Fundamenta Mathematicae 194, 2007, 253-265. .dvi file, LaTeX file.
- (with G. Sargsyan) “A Reduction in Consistency Strength for Universal Indestructibility”, Bulletin of the Polish Academy of Sciences (Mathematics) 55, 2007, 1-6. .dvi file, LaTeX file.
- (with J. Cummings and J. D. Hamkins) “Large Cardinals with Few Measures”, Proceedings of the American Mathematical Society 135, 2007, 2291-2300. .dvi file, LaTeX file.
- “Reducing the Consistency Strength of an Indestructibility Theorem”, Mathematical Logic Quarterly 54, 2008, 288-293. .dvi file, LaTeX file.
- (with J. Cummings) “An L-like Model Containing Very Large Cardinals”, Archive for Mathematical Logic 47, 2008, 65-78. .dvi file, LaTeX file.
- “Indestructibility and Measurable Cardinals with Few and Many Measures”, Archive for Mathematical Logic 47, 2008, 101-110. .dvi file, LaTeX file.
- (with G. Sargsyan) “Universal Indestructibility for Degrees of Supercompactness and Strongly Compact Cardinals”, Archive for Mathematical Logic 47, 2008, 133-142. .dvi file, LaTeX file.
- (with P. Koepke) “Making All Cardinals Almost Ramsey”, Archive for Mathematical Logic 47, 2008, 769-783. .dvi file, LaTeX file.
- “On the Number of Normal Measures $\aleph_1$ and $\aleph_2$ can Carry”, Tbilisi Mathematical Journal 1, 2008, 9-14. Note: This paper may be accessed online at http://ncst.org.ge/Journals/TMJ/ by clicking on the link “Most recent volume”. .dvi file, .pdf file, LaTeX file.
- “A Note on Indestructibility and Strong Compactness”, Bulletin of the Polish Academy of Sciences (Mathematics) 56, 2008, 191-197. .dvi file, .pdf file, LaTeX file.
- “Stationary Reflection and Level by Level Equivalence”, Colloquium Mathematicum 115, 2009, 113-128. .dvi file, .pdf file, LaTeX file.
- “Indestructibility and Stationary Reflection”, Mathematical Logic Quarterly 55, 2009, 228-236. .dvi file, .pdf file, LaTeX file.
- “Indestructibility under Adding Cohen Subsets and Level by Level Equivalence”, Mathematical Logic Quarterly 55, 2009, 271-279. .dvi file, .pdf file, LaTeX file.
- “Indestructibility, Strong Compactness, and Level by Level Equivalence”, Fundamenta Mathematicae 204, 2009, 113-126. .dvi file, .pdf file, LaTeX file.
- “Sandwiching the Consistency Strength of Two Global Choiceless Cardinal Patterns”, Bulletin of the Polish Academy of Sciences (Mathematics) 57, 2009, 189-197. .dvi file, .pdf file, LaTeX file.
- “L-like Combinatorial Principles and Level by Level Equivalence”, Bulletin of the Polish Academy of Sciences (Mathematics) 57, 2009, 199-207. .dvi file, .pdf file, LaTeX file.
- “Tallness and Level by Level Equivalence and Inequivalence”, Mathematical Logic Quarterly 56, 2010, 4-12. .dvi file, .pdf file, LaTeX file.
- (with G. Sargsyan) “An Equiconsistency for Universal Indestructibility”, Journal of Symbolic Logic 75, 2010, 314-322. .dvi file, .pdf file, LaTeX file.
- “How Many Normal Measures Can $\aleph_{\omega_1 + 1}$ Carry?”, Mathematical Logic Quarterly 56, 2010, 164-170. .dvi file, .pdf file, LaTeX file.
- (with P. Koepke) “The Consistency Strength of Choiceless Failures of SCH”, Journal of Symbolic Logic 75, 2010, 1066-1080. .dvi file, .pdf file, LaTeX file.
- “Indestructibility, Instances of Strong Compactness, and Level by Level Inequivalence”, Archive for Mathematical Logic 49, 2010, 725-741. .dvi file, .pdf file, LaTeX file.
- “Indestructibility, HOD, and the Ground Axiom”, Mathematical Logic Quarterly 57, 2011, 261-265. .dvi file, .pdf file, LaTeX file.
- “A Remark on the Tree Property in a Choiceless Context”, Archive for Mathematical Logic 50, 2011, 585-590. .dvi file, .pdf file, LaTeX file.
- (with Sh. Friedman) “Coding into HOD via Normal Measures with Some Applications”, Mathematical Logic Quarterly 57, 2011, 366-372. .dvi file, .pdf file, LaTeX file, .bib file.
- “Level by Level Inequivalence beyond Measurability”, Archive for Mathematical Logic 50, 2011, 707-712. .dvi file, .pdf file, LaTeX file.
- “Indestructibility, Measurability, and Degrees of Supercompactness”, Mathematical Logic Quarterly 58, 2012, 75-82. .dvi file, .pdf file, LaTeX file.
- (with V. Gitman and J. D. Hamkins) “Inner Models with Large Cardinal Features Usually Obtained by Forcing”, Archive for Mathematical Logic 51, 2012, 257-283. .dvi file, .pdf file, LaTeX file, .bib file.
- “Some Applications of Sargsyan’s Equiconsistency Method”, Fundamenta Mathematicae 216, 2012, 207-222. .dvi file, .pdf file, LaTeX file.
- “The Wholeness Axioms and the Class of Supercompact Cardinals”, Bulletin of the Polish Academy of Sciences (Mathematics) 60, 2012, 101-111. .dvi file, .pdf file, LaTeX file.
- (with M. Gitik and G. Sargsyan) “Indestructible Strong Compactness but not Supercompactness”, Annals of Pure and Applied Logic 163, 2012, 1237-1242. .dvi file, .pdf file, LaTeX file.
- “Level by Level Inequivalence, Strong Compactness, and GCH”, Bulletin of the Polish Academy of Sciences (Mathematics) 60, 2012, 201-209. .dvi file, .pdf file, LaTeX file.
- “More Easton Theorems for Level by Level Equivalence”, Colloquium Mathematicum 128, 2012, 69-86. .dvi file, .pdf file, LaTeX file.
- “On Some Questions Concerning Strong Compactness”, Archive for Mathematical Logic 51, 2012, 819-829. .dvi file, .pdf file, LaTeX file.
- (with S. Jackson and B. Loewe) “Cofinality and Measurability of the First Three Uncountable Cardinals”, Transactions of the American Mathematical Society 365, 2013, 59-98. .dvi file, .pdf file, LaTeX file, .bib file.
- (with B. Cody) “Consecutive Singular Cardinals and the Continuum Function”, Notre Dame Journal of Formal Logic 54, 2013, 125-136. .dvi file, .pdf file, LaTeX file.
- (with J. Cummings and J. D. Hamkins) “Singular Cardinals and Strong Extenders”, Central European Journal of Mathematics 11, 2013, 1628-1634. .dvi file, .pdf file, LaTeX file.
- “Indestructible Strong Compactness and Level by Level Inequivalence”, Mathematical Logic Quarterly 59, 2013, 371-377. .dvi file, .pdf file, LaTeX file.
- “Some Remarks on Tall Cardinals and Failures of GCH”, Bulletin of the Polish Academy of Sciences (Mathematics) 61, 2013, 97-106. .dvi file, .pdf file, LaTeX file.
- “A Note on Powers of Singular Strong Limit Cardinals”, Infinity, Computability, and Metamathematics: Festschrift celebrating the 60th birthdays of Peter Koepke and Philip Welch, College Publications, Volume 23, 2014, 1-3. .dvi file, .pdf file, LaTeX file.
- “Singular Failures of GCH and Level by Level Equivalence”, Bulletin of the Polish Academy of Sciences (Mathematics) 62, 2014, 11-21. .dvi file, .pdf file, LaTeX file.
- (with M. Gitik) “On Tall Cardinals and Some Related Generalizations”, Israel Journal of Mathematics 202, 2014, 343-373. .dvi file, .pdf file, LaTeX file.
- “Inaccessible Cardinals, Failures of GCH, and Level by Level Equivalence”, Notre Dame Journal of Formal Logic 55, 2014, 431-444. .dvi file, .pdf file, LaTeX file.
- (with P. Koepke and I. Dimitriou) “The First Measurable Cardinal can be the First Uncountable Regular Cardinal at Any Successor Height”, Mathematical Logic Quarterly 60, 2014, 471-486. .pdf file, LaTeX file, .bib file.
- (with Sh. Friedman) “HOD-Supercompactness, Indestructibility, and Level by Level Equivalence”, Bulletin of the Polish Academy of Sciences (Mathematics) 62, 2014, 197-209. .dvi file, .pdf file, LaTeX file, .bib file.
- “A Universal Indestructibility Theorem Compatible with Level by Level Equivalence”, Archive for Mathematical Logic 54, 2015, 463-470. .pdf file, LaTeX file.
- “Indestructibility and Destructible Measurable Cardinals”, to appear in the Archive for Mathematical Logic (the special volume in honor of Richard Laver). .dvi file, .pdf file, LaTeX file.
- “On the Consistency Strength of Level by Level Inequivalence”, to appear in the Archive for Mathematical Logic (the special volume in honor of Jim Baumgartner). .dvi file, .pdf file, LaTeX file.
- (with P. Koepke and I. Dimitriou) “All Uncountable Cardinals in the Gitik Model are Almost Ramsey and Carry Rowbottom Filters”, to appear in the Mathematical Logic Quarterly. .pdf file, LaTeX file, .bib file.
- “Indestructibility and the Levinski Property”, to appear in the Sarajevo Journal of Mathematics. .pdf file, LaTeX file.
- “Mixed Levels of Indestructibility”, submitted for publication to Bulletin of the Polish Academy of Sciences (Mathematics). .dvi file, .pdf file, LaTeX file.
- “Indestructible Strong Compactness and Level by Level Equivalence with No Large Cardinal Restrictions”, submitted for publication to Bulletin of the Polish Academy of Sciences (Mathematics). .pdf file, LaTeX file.
- “Precisely Controlling Level by Level Behavior”, submitted for publication to the Mathematical Logic Quarterly. .pdf file, LaTeX file.
- “A Note on Tall Cardinals and Level by Level Equivalence”, submitted for publication to the Mathematical Logic Quarterly. .pdf file, LaTeX file.

]]>

Students who need to take these courses receive a letter in June inviting them to register. It is strongly recommended that invited students participate in this tuition **free** program, it is required for SEEK and Prelude students.

The program begins after the July 4th break, and is offered in both the day and evening. The day program includes regular classroom instruction, tutoring and computer assisted instruction. The evening component has longer classroom instruction as it does contain tutoring or computer assisted instruction. The program runs six weeks, ending in mid August.

The courses offered in the Program are:

FSPM 0121: This course is identical in content to CSTM 0120 and covers topics in intermediate algebra. Students placed into this course have demonstrated a knowledge of elementary algebra. Students completing this course may register for MTH 1030 – College Algebra, in the fall.

FSPM 1031: This is a college algebra course, identical in content with MTH 1030. Students completing this course may register for MTH 2003 – Precalculus with Elements of Calculus, in the fall.

]]>Anita Mayo received a BA from Barnard College and a Ph.D. in mathematics from the Courant Institute, NYU. Her areas of specialization are numerical analysis, applied mathematics and, more recently, computational finance. In her work she has developed rapid and highly accurate methods for solving a variety of differential equations on general regions. She has applied these techniques to solving problems in elasticity, electrodynamics and fluid mechanics, including ones directly arising in the manufacture of IBM chips and recording devices. In particular she has helped engineers develop programs used for modeling deposition in CMOS manufacture and programs that were widely used for modeling thin film recording heads. She has also developed rapid methods for pricing certain financial options.

** Publications **

Mayo, A, * On the numerical evaluation of option prices in the Variance* *Gamma model*, International Journal of Computer Mathematics, 86(2) Feb. 2009, pp. 86-99.

Mayo, A., *Methods for the pricing of PIDEs in Exponential and Merton Models, *Journal of Computational and Applied Math., vol. 222, issue 1, December 2008, 128-143.

P. Carr and A. Mayo, On the numerical evaluation of option prices in jump diffusion models European Journal of Finance, vol.13, issue 4 June 2007, 353- 369.

Mayo, A. and Greenbaum, A. *Fourth order accurate evaluation of integrals in potential theory on exterior 3d regions,* J. of Computational Phys., vol 220, Issue 2, January 2006, pp. 900-914.

Mayo, A., *Rapid fourth order accurate solution of the steady Navier Stokes ** equations on general regions,* Dynamics of Continuous, Discrete and Impulsive Systems, Series B, 12, 2005, pp.59-72.

Mayo, A*., High Order Accurate Implicit Method for Valuing American Options *The European Journal of Finance, vol. 10, no.3, 2004, pp. 212-237.

Ruehli, A., Antonini, G., Esch, J., Mayo, A. and Orlandi, A., *Non Orthogonal PEEC Formulation for Time and Frequency Domain EM and Circuit Modeling*, IEEE Transactions Electro-Magnetic Compatibility, vol. 45, no.2, 2003, 167-.179.

Mayo, A.,* Rapid, fourth order accurate evaluation of particular solutions of the biharmonic equation on general regions*, Contemporary Mathematics, American Mathematical Association (AMS), vol.323, 2003, pp 233-245.

Greenbaum, A. and Mayo, A., *Rapid Parallel Evaluation of Integrals in Potential Theory** on General Three Dimensional Regions*, J. of Computational Phys, 145, 1998, pp. 731-742.

Mayo,A.,* Deferred Correction Finite Difference Methods for the Evaluation of Integrals in Potential Theory and Low Frequency Scattering,* Integral methods in Science and Engineering,Vol. 2, Addison Wesley, 1997, pp.165-170.

Mayo, A., Hamaguchi , S., Rossnagel, S. and Joo, J., *Across wafer nonuniformity of long throw sputter deposition systems*, Journal of the Vacuum Society B. Vol. 15, October 1997, pp. 1788-1793.

Hamaguchi, S., Mayo, A., Rossnagel, S., Kotecki, D. and Milkove, K, *Numerical Simulation of Etching and Deposition Processes*, J. Journal Applied Physics,Vol. 36, No. 7B, 1997, pp. 4762 – 4768.

Greengard, L., Kropinski, M. C. and Mayo, A., *Integral equation methods for Stokes flow and isotropic elasticity in the plane*, J. of Computational Physics, v. 125, May 1996, pp. 403-41

McKenney, A., Greengard, L. and Mayo, A., *A fast Poisson solver for complex geometries,* J. of Computational Physics, Vol. 118, 1995, pp. 348-355.

** **Li, Z. and Mayo, A., *ADI Methods for heat equations with discontinuities along an arbitrary interface*, Symposia in Applied Mathematics, American Mathematics Society (AMS), Vol. 48, 1994, pp.311-333.

Mayo, A., and. Peskin, C., *An implicit numerical method for fluid dynamics problems with immersed elastic boundaries*, Contemporary Mathematics, American Mathematical Society (AMS), Vol. 141, 1993, pp. 261-277.

Mayo, A., *The rapid evaluation of volume integrals of potential theory on genera regions,* J. of Computational Physics, Vol. 100, No. 2, June 1992, pp.236- 245.

Greenbaum, A., Greengard, L. and Mayo, A., *On the numerical solution of the **biharmonic equation in the plane,* Physica D, 60, 1992, pp. 216-225.

PATENTS

__ __Mayo, A. and Rubin, B., Method for determining voltage, current and/or power distributions in a resistive structure using a rectangular grid algorithm modified for nonrectangular holes and contacts, Patent No. US 6,704, 669B2, Date of patent: May 9, 2004.

**Research Interests **

My current research falls into two broad areas of application of probability theory: spatially disordered systems, and computational finance.

Spatially disordered systems is a class of probabilistic models generally motivated by physical problems arising in condensed matter physics and materials science. Two types of systems that I study are called first-passage percolation (FPP) and stochastic Ising dynamics. FPP has applications in areas as seemingly diverse as properties of porous media (aquifers, membranes, etc.), the growth of cancerous tumors, the propagation of cracks through concrete, and the flow of electricity through networks. Ising models capture some of the fundamental features of magnetized materials.

My work in computational finance generally focuses on the application of probabilistic methods and arbitrage-free pricing theory in valuing financial instruments and quantifying risk. It is practical in nature, much of it motivated directly by industry applications.

**Mathematics Papers**

Models of First-Passage Percolation, (C.D. Howard), Probability on Discrete Structures, (H. Kesten, Ed.), Springer-Verlag, 2004, 125 – 174.

The Percolation Transition for the Zero-Temperature Stochastic Ising Model on the Hexagonal Lattice, (C. D. Howard and C. M. Newman), Journal of Statistical Physics, 111(2003), 57 – 72.

Differentiability and Monotonicity of Expected Passage Time in Euclidean First-Passage Percolation, (C.D. Howard), Journal of Applied Probability, 38(2001), 815-827.

Geodesics and Spanning Trees for Euclidean Models of First-Passage Percolation, (C.D. Howard and C.M. Newman), Annals of Probability, 29(2001), 577-623.

Lower Bounds for Point-to-Point Wandering Exponents in Euclidean First-Passage Percolation, (C.D. Howard), Journal of Applied Probability, 37(2000), 736-747.

Zero-Temperature Ising Spin Dynamics on the Homogeneous Tree of Degree Three, (C.D. Howard), Journal of Applied Probability, 37(2000), 736-747.

From Greedy Lattice Animals to Euclidean Models of First-Passage Percolation, (C.D. Howard and C.M. Newman), Perplexing Problems in Probability: Papers in Honor of Harry Kesten, Birkhauser (M. Bramson and R. Durrett, Eds.), 1999.

Good Paths Don’t Double Back, (C.D. Howard), The American Mathematical Monthly, 105(1998), 354-357.

Euclidean Models of First-Passage Percolation, (C.D. Howard and C.M. Newman), Probability Theory and Related Fields, 108(1997), 153-170.

Distinguishing Certain Random Sceneries on Z via Random Walks, (C.D. Howard), Statistics and Probability Letters, 34(1997), 123-132.

Orthogonality of Measures Induced by Random Walks with Scenery, (C.D. Howard), Combinatorics, Probability, & Computing, 5(1996), 247-256.

Detecting Defects in Periodic Scenery by Random Walks on Z, (C.D. Howard), Random Structures and Alogrithms, 8(1996), 59-74.

**Computational Finance Papers**

Obtaining Distributional Information from Valuation Lattices, (C.D. Howard), Applied Mathematical Finance, 7(2000), 101-114.

Numerical Pitfalls of Latticed-Based Duration and Convexity Calculations, (C.D. Howard), Advances in Fixed-Income Valuation Modeling and Risk Management, Frank J. Fabozzi Associates, 1996, 327-336.

Valuing Path-Dependent Securities: Some Numerical Examples, (C.D. Howard), Advances in Fixed-Income Valuation Modeling and Risk Management, Frank J. Fabozzi Associates, 1996, 49-68. Also appears in: Investment Management for Insurers, (D.F. Babbel and F.J. Fabozzi, eds.) Frank J. Fabozzi Associates, 1999, 269-286.

Embedded Call Options and Refunding Efficiency, (C.D. Howard and A.J. Kalotay), Advances in Futures and Options Research, Vol. 3 (F.J. Fabozzi, ed.) JAI Press Inc, 1988, 97-117.

Long-Term Debt and Equity Markets and Instruments, (C.D. Howard and A.J. Kalotay) Handbook of Financial Markets and Institutions, (E.I. Altman, ed.) John Wiley & Sons, 1987, 5.1-5.37.

]]>**He can be found in VC-6-285 or VC-10-130.**

**12:25pm-2:05pm, Monday and Wednesday, VC-10-130**

Numerical Methods for Differential Equations in Finance

**2:55pm-4:35pm, Wednesday, VC-10-130**

Vector Calculus

**5:40pm-7:20pm, Monday and Wednesday, VC-10-130**

Mathematical Probability

**3:00pm-5:00pm, Thursday, VC-6-285**

Office Hours

**3:00pm-4:00pm, Tuesday, VC-6-285**

Research Meeting

**3:00pm-4:00pm, Friday, VC-6-285**

Research Meeting

**Projects**

New Methods for Fractional Black-Scholes Equations

A New Operator Splitting Method for American Options

A New Spectral Method for American Options

GPU Acceleration for Numerical Methods

**Review Services**

Applied Numerical Mathematics, Computers & Mathematics with Applications, Numerical Methods for Partial Differential Equations, BIT Numerical Mathematics, Journal of Computational Physics, Journal of Scientific Computing, Symmetry, East Asian Journal on Applied Mathematics, SpringerPlus, Entropy, Journal of Computational and Applied Mathematics, Electronic Transactions on Numerical Analysis, SIAM Journal on Applied Mathematics, Computational Geosciences, SIAM Journal on Scientific Computing.

J. Kynčl, J. Pach, R. Radoičić, G. Tóth. (2015). Saturated simple and k-simple topological graphs, Computational Geometry: Theory and Applications, Volume 48(4), pp. 295-310. click here.

E. Ackerman, J. Pach, R. Pinchasi, R. Radoičić, G. Tóth. (2014). A note on coloring line arrangements, The Electronic Journal of Combinatorics, Volume 21(2), p. 2-23. click here

J. Pach, R. Radoičić, G. Tóth. (2012). Tangled thrackles, in: Computational Geometry (XIV Spanish Meeting on Computational Geometry, EGC, Alcalá de Henares, Spain, June 27-30, 2011), Lecture Notes in Computer Science Festschrift Volume in Honour of Ferran Hurtado’s 60th Birthday, Volume 7579, Springer-Verlag, pp. 45-53; also in: Geombinatorics, Volume 21(4), pp. 157-169. click here.

J. Fox, M. Mahdian, R. Radoičić. (2008). Rainbow solutions to the Sidon equation, Discrete Mathematics, Volume 308, pp. 4773-4778. click here.

R. Radoičić. G. Tóth. (2008). The discharging method in combinatorial geometry and the Pach-Sharir conjecture, in: Surveys on Discrete and Computational Geometry: Twenty Years Later (eds. J. E. Goodman, J. Pach, R. Pollack), Contemporary Mathematics, Volume 453, American Mathematical Society, pp. 319-342. click here.

J. Pach, R. Radoičić, G. Tardos, G. Tóth. (2006). Improving the crossing lemma by finding more crossings in sparse graphs, Discrete and Computational Geometry, Special Issue (devoted to SoCG 2004), Volume 36, pp. 527-552. click here

J. Pach, R. Radoičić, J. Vondrák. (2006). On the diameter of separated point sets with many nearly equal distances, European Journal of Combinatorics, Volume 27, pp. 1321-1332. click here

N. Alon, R. Radoičić, B. Sudakov, J. Vondrák. (2006). A Ramsey-type result for the hypercube, Journal of Graph Theory, Volume 53, pp. 196-208. click here

R. Pinchasi, R. Radoičić, M. Sharir. (2006). On empty convex polygons in a planar point set, Journal of Combinatorial Theory, Series A, Volume 113, pp. 385-419. click here

R. Pinchasi, R. Radoičić. (2004). Topological graphs with no self-intersecting cycle of length 4, in: Towards a Theory of Geometric Graphs, Contemporary Mathematics, Volume 342, American Mathematical Society, pp. 233-243. click here

]]>Students who need to take these courses will be contacted by the college and will be provided registration information. This is a tuition-free program (students are required to purchase the text). Students who enroll in this program **may not take any courses in the second summer session program.**

The program begins just after the July 4 holiday, concludes six weeks later in mid-August, and is offered in both the day and evening. The day program includes regular classroom instruction, tutoring and computer assisted instruction. The evening component has longer classroom instruction as it does contain tutoring or computer assisted instruction.

FSPM 0121: This course is identical in content to CSTM 0120 and covers topics in intermediate algebra. Students placed into this course have demonstrated a knowledge of elementary algebra. Students completing this course may register for MTH 1030 – College Algebra, in the fall.

FSPM 1031: This is a college algebra course, identical in content with MTH 1030. Students completing this course may register for MTH 2003 – Precalculus with Elements of Calculus, in the fall.

Students who successfully complete FSPM 0121 receive exemption from CSTM 0120 and may register for MTH 1030 in the fall.

Continuing Students who previously failed MTH 1030 and pass FSPM 1031 will have their grade replaced with a P and the college’s “F” policy will be applied. There will be no credit for the previously taken course and a comment will be placed on each student’s record to explain the application of the “F” policy without the repetition of the same course.

Click here to return to the Immersion Web Page

]]>