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Research Interests
I am a mathematician working at HP Labs. My work is a mix of
basic research and applied industrial research. My current
project at HP deals with algorithms for information management using
techniques from machine learning and data mining. My areas of
interest are the following:
- Number theory and
algebraic geometry, with applications to coding theory
- Machine learning and
data mining, with applications to information management
- Mathematical logic and
its role in theoretical computer science
- Stochastic processes
with applications to modeling and randomized algorithms
- Statistics with
applications to database estimation algorithms
- Digital communications,
with applications to wireless communication
Selected Publications
My research can be broadly divided into
basic and industrial.
BASIC RESEARCH
Vinay
Deolalikar. P ≠ NP.
The
preliminary version was
meant to solicit feedback from a few
researchers as is customarily done. It illustrated the interplay of
principles from various areas, which was the major effort in
constructing the proof. I have fixed all the issues that were raised
about the preliminary version in a revised manuscript;
clarified some concepts; and obtained simpler proofs of several
claims. Once I hear back from the journal as part of due process,
I
will
put up the final version on this website.
Deolalikar, Vinay. Ring theoretic
study of linear codes using additive polynomials. Finite fields
and applications, 91--102, Contemp. Math., 461, Amer. Math.
Soc., Providence, RI, 2008. MR2436327
(2010a:94108)
Deolalikar, Vinay; Hamkins, Joel David; Schindler, Ralf. ${\rm P}\neq{\rm
NP}\cap$ co-NP for infinite time Turing machines. J. Logic Comput.
15 (2005),
no.
5,
577--592.
MR2172411 (2006k:68026)
Deolalikar, Vinay. Explicitly
constructed extensions of the rational function field with prescribed
splitting. Finite Fields Appl. 9 (2003), no. 2, 222--236. MR1968032
(2004c:11215)
Deolalikar, Vinay. Determining
irreducibility and ramification groups for an additive extension of the
rational function field. J. Number Theory 97 (2002), no. 2, 269--286. MR1942960
(2004d:11114)
Deolalikar, Vinay. Extensions of
algebraic function fields with complete splitting of all rational
places. Comm. Algebra 30 (2002),
no.
6,
2687--2698.
MR1908233 (2003f:14019)
Aleshnikov,
Ilia; Deolalikar, Vinay; Kumar, P. Vijay; Stichtenoth, Henning.
Towards a basis for the space of regular functions in a tower of
function fields meeting the Drinfel'd-Vladut bound. Finite
fields
and
applications, Springer, Berlin, 2001. (Outstanding Research Paper Award: USC
Electrical Engineering-Systems, 2000).
INDUSTRIAL
RESEARCH
I have worked on several projects that require analysis of mathematical
models for various systems.
Lillibridge,
Mark; Eshghi, Kave; Bhagwat, Deepavali; Deolalikar, Vinay; Trezis,
Greg; Gamble, Peter. Sparse Indexing: Large Scale, Inline Deduplication
Using Sampling and Locality.
FAST 2009. pp.111--123
Deolalikar,
Vinay; Laffitte, Hernan. Provenance as data mining: combining file
system metadata with content analysis." Theory and applications of
Provenance 2009.
Deolalikar,
Vinay; Choudur, Lakshminarayan; Laffitte, Hernan. A new composite
estimator of distinct values that performs well in a wide range of
skewness." HP Labs Technical report 2008.
Deolalikar,
Vinay, Eshghi, Kave; Laffitte, Hernan. A lightweight distributed
algorithm based on order statistics to answer top-k queries." HP Labs
Technical report 2007.
Deolalikar,
Vinay. Timed Markov models and their Laplace transforms, with
applications to reliability models." HP Labs Technical report 2006.
Mathematics Lectures
(Stanford
University)
and
Notes
Notes from some lectures I
have given in the broad areas of Algebraic Geometry and Number Theory
at Stanford Mathematics:
- Modular
Forms and Modular Curves (3 lectures, 2000-2001)
- Moduli
Spaces of Curves and Teichmuller theory (4 lectures, 2004)
- Lecture
1: Low genus (0 and 1), construction of M_1
- Lecture
2: Orbifolds, Teichmuller space, Mapping class groups, Fenchel
Nielsen coordinates
- Lecture
3: Divisors, Line bundles, and Chern classes,
- Lecture
4: Algebraic cycles, Chow Groups, Hodge Theory (intro)
- Hodge
Theory (3 lectures, 2004)
- Lecture
1: Hodge theory on Riemann manifolds, de Rham theorem, Laplace
Beltrami, Harmonic forms, Dolbeault, Bott Chern cohomology
- Lecture
2: Hodge theory on Hermitian manifolds and Kahler manifolds, Hard
Lifschitz, Weak Lifschitz
- Lecture
3: Mixed Hodge structures, Leray Spectral sequence,
semi-simplicity, Lifschitz decomposition
Self-study notes on some areas in Logic:
- Elementary
Equivalence, Partial Isomorphism, and Scott-Karp analysis (self-study
notes)
Brief Bio
Born in 1971
in New Delhi, India. Married with two children. Other
interests include historical and
religious aspects of Hindu Dharma. Indian citizen.
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