Daniel M. Kane

Department Address:

Harvard University, Department of Mathematics

1 Oxford Street

Cambridge MA 02139, USA.

 

Office: Science Center 536

I am a Harvard math grad student with the funding of the NDSEG fellowship. I also have some interests in algorithms and physics.  My username is dankane and you can email me at username @alum.mit.edu, or @math.harvard.edu, I also have a gmail account with username ALadKeenIn.

Research

I have done a fair bit of research in Mathematics and Theoretical Computer Science.

Publications (links are .pdf):

·         Jeffery S. Cohen, and Daniel M. Kane Bounds on the Independence Required for Cuckoo Hashing, submitted to Algorithmica.

·         Ilias Diakonikolas, Daniel M. Kane, Jelani Nelson, Bounded Independence Fools Degree-2 Threshold Functions, submitted to ACM Symposium on Theory of Computing (STOC), 2010.

·         Daniel M. Kane The Gaussian Surface Area and Noise Sensitivity of Degree-d Polynomials, submitted to Conference on Computational Complexity (CCC), 2010.

·         Daniel M. Kane, Samuel A. Kutin, Quantum Interpolation of Polynomials, submitted to Conference on Computational Complexity (CCC), 2010.

·         Daniel M. Kane, Jelani Nelson and David P. Woodruff A Space-Optimal Algorithm for the Distinct Elements Problem, submitted to PODS, 2010.

·         Daniel M. Kane, Jelani Nelson and David P. Woodruff On the Exact Space Complexity of Sketching and Streaming Small Norms, accepted for Symposium on Discrete Algorithms (SODA), 2010.

·         Chris Dodd, Phakawa Jeasakul, Anne Jirapattanakul, Daniel M. Kane, Becky Robinson, Noah Stein, and Cesar E. Silva Ergodic Properties of a Class of Discrete Abelian Group Extensions of Rank-One Transformations, to appear in Colloquium Mathematicum.

·         Erik D. Demaine, Dion Harmon, John Iacono, Daniel Kane, and Mihai Pǎtraşcu, The Geometry of Binary Search Trees, to appear in Proceedings of the 20th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2009), New York, New York, January 4–6, 2009.

·         Daniel Kane, Gregory N. Price, and Erik D. Demaine, A pseudopolynomial algorithm for Alexandrov's Theorem, to appear in Proceedings of the 11th Algorithms and Data Structures Symposium (WADS 2009), Banff, Alberta, Canada, August 21–23, 2009.

·         Daniel M. Kane On Solving Games Constructed Using Both Shortened and Continued Conjunctive Sums, submitted to Integers.

·         Daniel M. Kane A Partition of the Positive Reals into Algebraically Closed Subsets, unpublished.

·         Bakir Farhi, Daniel Kane New Results on the Least Common Multiple of Consecutive Integers, Proceedings of the AMS, 137 (2009), no. 6, pp. 1933-1939.

·         Daniel Kane, and Steven Sivek On the S_n-Modules Generated by Partitions of a Given Shape, The Electronic Journal of Combinatorics, 15 (2008).

·         Daniel M. Kane Improved Bounds on the Number of Ways of Expressing t as a Binomial Coefficient, Integers: Electronic Journal of Combinatorial Number Theory, Vol. 7 (2007), #A53 pp. 1-7.

·         Daniel M. Kane On Lower Bounds on the Size of Sums-of-Squares Formulas Journal of Number Theory, 128 (2008) pp. 639-644.

·         Dan Gulotta, Daniel M. Kane, Andrew Spann Electoral Redistricting with Moment of Inertia and Diminishing Halves Models(3.81 MB) UMAP Journal, Vol. 28 (2007)

·         Daniel M. Kane Weak Mixing of a Transformation Similar to Pascal, Colloquium Mathematicum, 108 (2007), no. 1, pp. 135-140.

·         Daniel M. Kane Asymptotics of McKay Numbers for Sn, Journal of Number Theory, 124 (2007) pp. 200-228.

·         Dan Gulotta, Daniel M. Kane, Andrew Spann Application of Min-Cost Flow to Airline Accessibility Services UMAP Journal, Vol. 27 (2006).

·         Daniel M. Kane Generalized Base Representations Journal of Number Theory, 120 (2006) pp. 92-100.

·         Daniel M. Kane and Jonathan M. Kane Dropping Lowest Grades Mathematics Magazine, (2006) 79 (June) pp. 181-189.

·         Daniel M. Kane An Elementary Derivation of the Asymptotics of Partition Functions The Ramanujan Journal, Vol. 11 (2006) no. 1 pp. 49-66.

·         Dan Gulotta, Daniel M. Kane, Andrew Spann Lane Changes and Close Following: Troublesome Tollbooth Traffic(6 MB) UMAP Journal, Vol. 26 (2005) no. 3. pp. 251-264.

·         Tim G. Abbott, Daniel M. Kane, Paul Valiant On the Complexity of Two-Player Win-Lose Games Foundations Of Computer Science (FOCS), 2005.

·         Timothy G. Abbott, Michael A. Burr, Timothy M. Chan, Erik D. Demaine, Martin L. Demaine, John Hugg, Daniel Kane, Stefan Langerman, Jelani Nelson, Eynat Rafalin, Kathryn Seyboth, and Vincent Yeung, Dynamic Ham-Sandwich Cuts in the Plane, Computational Geometry: Theory and Applications, volume 42, number 5, July 2009, pages 419–428. Special issue of selected papers from the 17th Canadian Conference on Computational Geometry, 2005.

·         Tim Abbott, Erik D. Demaine, Martin L. Demaine, Daniel M. Kane, Setfan Langerman, Jelani Nelson,Vincent Yeung Dynamic Ham-Sandwich Cuts of Polygons in the Plane Proceedings of the 17th Canadian Conference on Computational Geometry, (2005) pp. 61-64.

·         Daniel M. Kane On the Number of Ways of Writing t as a Product of Factorials Integers: Electronic Journal of Combinatorial Number Theory, Vol. 5 (2005), #A02, pp. 1-10.

·         Daniel M. Kane Resolution of a Conjecture Involving Cranks of Partitions of Andrews and Lewis Proceedings of the American Mathematical Society, Vol. 132 (2004) No. 8, pp. 2247-2256.

·         Daniel M. Kane New Bounds on the Number of Representations of t as a Binomial Coefficient Integers: Electronic Journal of Combinatorial Number Theory, Vol. 4 (2004), #A07, pp. 1-10.

Talks (links are .ppt):

·         Dan Gulotta, Daniel Kane, and Andrew Spann, Electoral Redistricting with Moment of Inertia and Diminishing Halves Models (pdf) SIAM meeting July 2008.

·         Daniel M. Kane The Number of Ways of Expressing t as a Binomial Coefficient Joint Mathematics Meetings, January 2007.

·         Daniel M. Kane On Solving Games Constructed Using Both Shortened and Continued Conjunctive Sums Joint Mathematics Meetings, January, 2006.

·         Daniel M. Kane Ergodic Properties of Group Extensions of Rank 1 Transformations Part II Mathfest, August, 2004.

Coauthors: Tim Abbott, Michael A. Burr, Timothy M. Chan, Jeffery Cohen, Erik Demaine, Martin Demaine, Ilias Diakonikolas, Chris Dodd, Bakir Farhi, Dan Gulotta, John Hugg, John Iacono, Phakawa Jeasakul, Anne Jirapattanakul, Jonathan Kane, Samuel A. Kutin, Setfan Langerman, Jelani Nelson, Mihai Pǎtraşcu, Eynat Rafalin, Becky Robinson, Kathryn Seyboth, Cesar E. Silva, Andrew Spann, Noah Stein, Paul Valiant, David P. Woodruff, Vincent Yeung

Summer Programs

Here are some summer programs in which I have participated.

·         I spent summers of 2007, 2008, 2009 working at CCR-Princeton.

·         I spent summer 2006 working with Erik Demaine on problems in theoretical computer science.

·         Duluth REU, the undergraduate research program in Duluth. I participated the summer of 2005 and briefly in 2003 and 2006.

·         SMALL Program, the REU at Williams College. I participated during the summer of 2004.

·         Math Olympiad Summer Program, the training camp for the United States Math Olympics Team. I participated during the summers 1999-2003, and competed in the International Mathematical Olympiad in 2002, 2003.

·         US Physics Team, the training camp for the United States Physics Olympics Team. I participated during the summer of 2002.

Books contributed to:

·         USA & International Mathematical Olympiads 2003, Andreescu, T., Feng, Z, and Loh, P.-S., editors, MAA, 2004.

·         Mathematical Olympiads 2001-2002: Problems and Solutions from Around the World, Andreescu, T., Feng, Z, and Loh, P.-R., editors, MAA, 2004.

·         Mathematical Olympiads 2000-2001: Problems and Solutions from Around the World, Andreescu, T., Feng, Z, and Lee, G., Jr., editors, MAA, 2003.

·         Mathematical Olympiads 1999-2000: Problems and Solutions from Around the World, Andreescu, T., and Feng, Z, editors, MAA, 2001.

·         Mathematical Olympiads 1998-1999: Problems and Solutions from Around the World, Andreescu, T., and Feng, Z, editors, MAA, 2000.

Awards and Honors:

·         Won the Jon A. Bucsela prize for top senior in MIT's mathematics department.

·         Have NSF and NDSEG graduate fellowships.

·         Won the Frank and Brennie Morgan Prize for research by an undergraduate

·         Goldwater Fellow, 2006.

·         Co-winner of the Machtey Award for Best Student Paper at IEEE Symposium on Foundations of Computer Science, 2005.

·         Member of COMAP Mathematical Contest in Modeling Team 2004, 2005, 2006, 2007. Achieved an "Outstanding" in 2005, 2006, 2007. Won the Ben Fusaro Award for most creative solution in 2004. Won the INFORMS award in 2006 won the SIAM award in 2007.

·         Putnam Fellow (among top 5) 2003, 2004, 2005, 2006 and a Member of MIT's 1st place Team in 2003, 2004 in the William Lowell Putnam Mathematical Competition.

·         Fellow Laureate (among top 4) of Davidson Institute for Talent Development for prodigious work in mathematics, 2003.

·         2nd place, Math/Computer Sciences Section of National Junior Science and Engineering Symposium, 2003.

·         Gold Medalist at International Mathematical Olympiad as Member of USA Team, 2003, 2002

·         Akamai Scholar for Perfect Score on USA Mathematical Olympiad, 2002.

·         USAMO Award Winner (among top 12), 2003, 2002, 2001.

·         Perfect Score on Asian-Pacific Mathematical Olympiad, 2003.

·         USA Physics Olympiad Team qualifier (among top 24), 2003, 2002.

·         National Merit Scholar, National Merit Finalist, 2003.

·         Perfect score on Virginia Tech Intercollegiate Regional Mathematics Competition, 2002.

·         Gold Medalist (among top 25) in USA Math Talent Search, 2000.

·         Co-winner (one of 3) in University of Wisconsin Math Talent Search, 2000.

·         USAMO and Mathematical Olympiad Summer Program qualifier (among top 30), 1999-2003.

Degrees:

·         Bachelor of Science in Mathematics with Computer Science from MIT (June 2007)

·         Bachelor of Science in Physics from MIT (June 2007)

·         Master of Arts in Mathematics from Harvard (June 2008)

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Teaching Experience:

·         TA for 18.022 (Calc II) at MIT (Fall 2006)

·         TA for 18.03 (Differential Equations) at MIT (Spring 2007)

·         TF for Math Xa (Calc) at Harvard (Fall 2008)

·         TF for Math 21b (Linear Algebra/ Differential Equations) at Harvard (Fall 2009)