portraitDaniel M. Kane

Department Address:

Stanford University
Department of Mathematics
Building 380, Sloan Hall

Room 382-N
Stanford, California 94305

I am first year mathematics postdoc at Stanford currently funded by an NSF postdoctoral fellowship. I also have some interests in theoretical computer science.  My username is dankane and you can email me at this username @math.stanford.edu, @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.  Here is my thesis.

Publications (links are .pdf):

Mathematics:

·         Noam D. Elkies, Daniel M. Kane and Scott Duke Kominers, Minimal S-Criteria May Vary in Size, in revision.

·         Daniel M. Kane An Asymptotic for the Number of Solutions to Linear Equations in Prime Numbers from Specified Chebotarev Classes, in revision.

·         Daniel M. Kane Small Designs for Path Connected Spaces and Path Connected Homogeneous Spaces, submitted to Duke Mathematics Journal.

·         Daniel M. Kane On a Problem Relating to the ABC Conjecture, submitted to Journal of Number Theory.

·         Daniel M. Kane Canonical Projective Embeddings of the Deligne-Lusztig Curves Associated to 2A2, 2B2 and 2G2, submitted to Advances in Mathematics.

·         Daniel M. Kane On the Ranks of the 2-Selmer Groups of Twists of a Given Elliptic Curve, submitted to the Journal of Number Theory.

·         Daniel M. Kane and Scott Duke Kominers Asymptotic Improvements of Lower Bounds for the Least Common Multiples of Arithmetic Progressions, submitted to the Canadian Mathematical Bulletin.

·         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.

·         Daniel M. Kane On Solving Games Constructed Using Both Shortened and Continued Conjunctive Sums, to appear in 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·         Daniel M. Kane A Partition of the Positive Reals into Algebraically Closed Subsets, unpublished.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 Sn-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.

·         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.

Computer Science:

·         Daniel M. Kane, Kurt Mehlhorn, Thomas Sauerwald, and He Sun Counting Arbitrary Subgraphs in Data Streams, submitted to International Colloquium on Automata, Languages and Programming (ICALP 2012).

·         Eric Blais and Daniel Kane Testing Properties of Linear Functions, submitted to International Colloquium on Automata, Languages and Programming (ICALP 2012).

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

·         Daniel M. Kane, Jelani Nelson, Sparser Johnson-Lindenstrauss Transforms, Symposium on Discrete Algorithms (SODA 2012), to appear.

·         Daniel M. Kane, A Small PRG for Polynomial Threshold Functions of Gaussians, Foundations of Computer Science (FOCS 2011), to appear.

·         Daniel M. Kane, Raghu Meka, Jelani Nelson, Almost Optimal Explicit Johnson-Lindenstrauss Transforms, International Workshop on Randomization and Computation (RANDOM 2011), 2011.

·         Daniel Kane, Jelani Nelson, A Derandomized Sparse Johnson-Lindenstrauss Transform, superseded by Sparser Johnson-Lindenstrauss Transforms (above).

·         Daniel M. Kane k-Independent Gaussians Fool Polynomial Threshold Functions, Conference on Computational Complexity (CCC), 2011.

·         Daniel M. Kane, Jelani Nelson, Ely Porat, David P. Woodruff, Fast Moment Estimation in Data Streams in Optimal Space, Symposium on the Theory of Computing (STOC), 2011.

·         Daniel M. Kane, Samuel A. Kutin, Quantum Interpolation of Polynomials, presented at Combinatorics, Groups, Algorithms, and Complexity (conference in honor of Laci Babai’s 60th birthday (CGAC 2010)), to appear in Quantum Information and Computation.

·         Daniel M. Kane Unary Subset-Sum is in Logspace, unpublished.

·         Ilias Diakonikolas, Daniel M. Kane, Jelani Nelson, Bounded Independence Fools Degree-2 Threshold Functions, to appear in Foundations of Computer Science (FOCS), 2010.

·         Daniel M. Kane The Gaussian Surface Area and Noise Sensitivity of Degree-d Polynomial Threshold Functions, in Proceedings of the 25th annual IEEE Conference on Computational Complexity (CCC 2010), pp. 205-210.

·         Daniel M. Kane, Jelani Nelson and David P. Woodruff An Optimal Algorithm for the Distinct Elements Problem, Proceedings of the 29th Annual ACM Symposium on Principles of Database Systems (PODS 2010). Invited to Journal of the ACM.

·         Daniel M. Kane, Jelani Nelson and David P. Woodruff On the Exact Space Complexity of Sketching and Streaming Small Norms, Proceedings of the 21st Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2010).

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

·         Daniel Kane, Gregory N. Price, and Erik D. Demaine, A pseudopolynomial algorithm for Alexandrov's Theorem, Proceedings of the 11th Algorithms and Data Structures Symposium (WADS 2009), Banff, Alberta, Canada, August 21–23, 2009.  Also in Lecture Notes in Computer Science, 5664 (2009) pp. 435–446.

·         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.

Talks (links are .pdf):

·         Daniel M. Kane A Small PRG for Polynomial Threshold Functions of Gaussians, Symposium on the Foundations Of Computer Science (FOCS), 2011.

·         Daniel M. Kane Noise Sensitivity of Polynomial Threshold Functions, MSRI Workshop on Quantitative Geometry, 2011.

·         Daniel M. Kane k-Independence Fools Polynomial Threshold Functions of Gaussians, Conference on Computational Complexity (CCC), 2011.

·         Daniel M. Kane Ranks of 2-Selmer of Twists of an Elliptic Curve, South Eastern Regional Meeting on Numbers (SERMON), 2011.

·         Daniel M. Kane The FT-Mollification Method, Workshop on Analysis and Geometry of Polynomial Threshold Functions, 2010.

·         Daniel Kane The Gaussian Surface Area and Noise Sensitivity of Degree-d Polynomial Threshold Functions, CCC, 2010.

·         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, Eric Blais, Michael A. Burr, Timothy M. Chan, Jeffery Cohen, Erik Demaine, Martin Demaine, Ilias Diakonikolas, Chris Dodd, Noam Elkies, Bakir Farhi, Dan Gulotta, John Hugg, John Iacono, Phakawa Jeasakul, Anne Jirapattanakul, Jonathan Kane, Samuel A. Kutin, Setfan Langerman, Raghu Meka, Kurt Mehlhorn, Jelani Nelson, Mihai Pǎtraşcu, Eynat Rafalin, Becky Robinson, Thomas Sauerwald, Kathryn Seyboth, Cesar E. Silva, Andrew Spann, Noah Stein, He Sun, Paul Valiant, David P. Woodruff, Vincent Yeung

Summer Programs

Here are some summer programs in which I have participated.

·         Was an instructor at the US Mathematical Olympiad Summer Program, 2011.

·         I spent summer of 2010 as an intern at Microsoft Research New England

·         I spent summers of 2007, 2008, 2009, 2011 working at CCR.

·         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.  I was also an instructor for a week during 2011.

·         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:

·         Co-winner of one of the 2010 IBM research Pat Goldberg Memorial Best Paper Award in Computer Science, Electrical Engineering and Math awards.

·         PODS 2010 Best paper

·         CCC 2010 Best student paper

·         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)

·         Doctor of Philosophy in Mathematics from Harvard (June 2011)

Teaching Experience:

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

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

·         Teaching Fellow for Math Xa (Calc) at Harvard (Fall 2008)

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