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Steven J. Miller
Assistant Professor of Mathematics, Brown University
210 Kassar House, 401-863-1123 (sjmiller AT math.brown.edu)
Starting in Fall '08 I will be an assistant professor of mathematics
and statistics at Williams College. I can always be reached at Steven.Miller.MC.96 AT aya.yale.edu |
curriculum
vita
research statement
teaching statement
|
- RESEARCH INTERESTS:
Analytic Number Theory, Random Matrix Theory, Analysis and
Probability (distribution of zeros and n-level statistics for
families of L-functions, especially families of elliptic curves with rank over
Q(T), classical random matrix theory, random graphs, ranks of elliptic curves,
computational number theory, probability theory, Benford's Law, cryptography,
linear programming, multiple Dirichlet series).
Thesis
Papers
Talks
My Book (Invitation to Modern Number Theory)
Handouts
My
Riddles Page
If there are several versions of a talk, the later version is usually the
more 'complete' (ie, correct) version.
- Random Matrix Theory and L-Functions
- Random Matrix Theory and L-Functions I:
Analytic Number Theory Seminar,
Ohio State
(10/20/03):
pdf
- Random Matrix Theory and L-Functions II:
Analytic Number Theory Seminar,
Ohio State
(10/27/03):
pdf
- From Random Matrix Theory to L-Functions:
Special Number Theory Seminar, Tel Aviv
(12/23/04):
pdf
- Identifying Symmetry Groups of Zeros of Families of
L-Functions:
Number Theory and Random Matrix Theory
Workshop, CMS Summer 2005, Waterloo
(6/1/05):
ps
pdf;
tabbed version
ps
dvi
- Identifying and breaking the symmetry group of zeros of
families of L-functions:
Number Theory Seminar, CUNY Lehman
(10/20/06):
pdf
- A Symplectic Test of the L-Functions Ratios Conjecture:
Algebra Seminar,
Brown University
(9/17/07):
paper.pdf
AMS Special Session on L-functions and automorphic
forms, Courant (20 minute version, 3/16/08):
pdf
tabbed version
pdf
Johns Hopkins University (50 minute version, 4/4/08):
pdf
(untabbed version:
pdf); Cornell University (50 minute version, 6/5/08):
pdf
(untabbed version:
pdf).
- Random Matrix Theory and Elliptic Curves
- 1 and 2 Level Density Functions for Families
of Elliptic Curves: Evidence for the Underlying Group Symmetries.
(Thesis defense) Princeton (5/26/02), Number Theory
Seminar Ohio State (5/30/02):
pdf
Boston University (2/10/03):
pdf
- Evidence for a Spectral Interpretation of
the Zeros of Families of Elliptic Curves.
Joint meeting of the AMS and UMI
Pisa (6/13/02):
pdf
title
Shorter version (20 minutes):
AMS Sectional, Salt Lake City (10/27/02):
dvi
pdf
-
Random Matrix Theory and Elliptic Curves: Evidence for the
Underlying Group Symmetries (with three appendices). Johns Hopkins University (3/3/04):
pdf An alternate version:
Five College Number Theory Seminar,
Amherst, MA, (4/20/04):
pdf
-
Random Matrix Theory models for zeros near the central
point (and applications to elliptic curves) (45 minutes)
Workshop on Spectral Theory and
Automorphic Forms, Montréal, May 2004.
ps. An alternate version (60 minutes):
Boston University (2/10/03):
ps Brown University (9/13/04 - expanded):
dvi
pdf
Another alternate version: (120 minutes)
Fellowship of the Ring Seminar, Brandeis
University (4/1/05):
ps
pdf; tabbed
version ps
dvi.
Another alternate version (30 minutes),
Advances in Number Theory and Random Matrix
Theory, Rochester, NY (6/7/06):
pdf; tabbed
version pdf;
paper the
talk is based on (to appear in Experimental Mathematics)
-
How the Manhattan Project helps us understand primes and
elliptic curves (with
appendices on Dirichlet L-Fns, Random Graphs and a bibliography).
Colloquium, University of Connecticut (3/24/05):
ps
pdf;
tabbed version
ps
dvi.
-
From the Manhattan Project to Number Theory: How nuclear
physics helped us understand primes:
Theoretical Physics Seminar, Brown University (4/12/06):
pdf;
relevant papers: Investigations of Zeros Near the Central Point of Elliptic Curve
L-Functions (to appear in
Experimental Mathematics)
pdf
(data available
online).
-
Finite conductor models for zeros near the central point of
elliptic curve L-functions (with Eduardo Dueñez, Duc Khiem Huynh and Jon
P. Keating).
L-functions, ranks of elliptic curves and
random matrix theory workshop, Banff (7/12/07):
slides:
pdf (my part);
pdf (Dueñez);
ppt (Keating);
pdf (Huynh)
pdf (combined).
- Elliptic Curves
-
Ranks of One-Parameter Families of Elliptic Curves Over Q(T)
and Thoughts on the Excess Rank Question (with five appendices).
Boston College (3/10/03):
dvi
pdf
-
Constructing 1-Parameter Families of Elliptic Curves over
Q(T) with
Moderate Rank. AMS Sectional, Boulder, CO (10/4/03):
pdf
-
The effect of zeros of elliptic curve L-functions at the
central point on nearby zeros. AMS
Sectional, Lawrenceville, NJ
(4/18/04):
pdf Expanded
Version: Algebra Seminar, Brown University (10/24/05):
pdf
tabbed version
dvi
- Random Matrix Ensembles
- Eigenvalue Statistics for Ensembles of
Random Matrices (especially Toeplitz Ensembles &
Diophantine Obstructions).
Probability and Ergodic Theory Seminar,
Ohio State
(10/30/03):
pdf
Boston University (6/7/04 expanded):
pdf
Brown University (9/15/04 expanded):
pdf
- On the probability that random graphs are Ramanujan.
Expanders and Ramanujan Graphs: Construction and
Applications, AMS National Meeting, San Diego (1/9/08):
pdf
- Analysis and Probability (especially Benford's Law)
- Benford's Law, Values of
L-functions and the 3x+1 Problem. Boston College (10/19/04),
University of Michigan (11/15/04), University of Arizona (1/11/06),
Brown University (3/20/06): slides
paper.pdf
Mathematica programs:
Just
the 3x+1 Map
Benford
Investigations Some Numerical
Simulations:
Data
- Benford's Law and Order Statistics.
Brown University (2/1/06)
paper.pdf
- When almost all sets are difference dominated.
Analysis Seminar, Brown University (9/12/07)
paper.pdf
- Poisson Summation and Benford's Law: From values of L-functions to the
$3x+1$ problem to products of random variables.
University of Bristol (12/12/07); Workshop on the Theory and Applications of
Benford's Law, Santa Fe, NM (12/18/07):
pdf
- The logarithmic link between economic, hydrologic, and seismic
statistics (with Mark Nigrini),
Workshop on the Theory and Applications of Benford's Law, Santa Fe, NM (12/17/07):
- Chains of distributions and Benford's Law (with Dennis Jang, Jung Uk
Kang, Alex Kruckman and Jun Kudo),
Workshop on the Theory and Applications of Benford's Law, Santa Fe, NM (12/17/07):
pdf
- Benford's Law: Why the IRS might care about the 3x+1 problem and
ζ(s) (general introduction to the
subject),
Western New England College (2/11/08):
pdf (untabbed
version
pdf)
- Theory and applications of Benford's law to fraud detection, or: Why the
IRS should care about number theory! IRS (Boston
Offices, 3/28/08):
pdf (untabbed
version
pdf);
Dinner meeting of the Northeastern MAA (40 minute version, 4/28/08):
pdf.
Computers and Mathematics Education
- Computers in Undergraduate Education and Zeros of Elliptic
Curves.
Minnesota (8/10/02):
pdf
Expanded Version:
pdf
-
Statistical Investigations as a Tool in Undergraduate Mathematics
Research: Poster and Workshop Sessions
International Conference on Statistics Honolulu, Hawaii (6/5/03 and 6/7/03):
pdf
- NSF Workshop on Computation in Algebra, Number Theory and Combinatorics.
Washington DC (9/21/02):
ps
and
ps
-
The Pythagorean Won-Loss Theorem: An introduction to modeling.
Great Activities for an Introductory Statistics
Class, AMS National Meeting, San Diego, (1/7/08):
pdf
-
Workshop on Mathematicians in Mathematics Education, participant,
Institute for Mathematics Education,
Tucson, Arizona, March 20 - 22, 2008.
Colloquium Talks
-
How the Manhattan Project helped us understand primes.
Colloquium, University of Cincinatti
(10/16/03) and Ohio State (10/1/03):
pdf.
An alternate version (with appendices on Dirichlet L-Fns, Elliptic Curves
and a bibliography):
Colloquium, Colby College (3/8/05):
ps
pdf;
tabbed version
ps
dvi.
Another alternate version (with appendices on Dirichlet L-Fns, Random Graphs and a bibliography).
Colloquium, University of Connecticut (3/24/05):
ps
pdf;
tabbed version
ps
dvi
-
From Nuclear Physics to Number Theory: How the Manhattan
Project helped us understand Primes: SUMS
Conference, Brown University (2/12/05):
ps
pdf;
tabbed version
ps
dvi
This is similar to the above colloquia, but aimed more at undergraduates.
-
L-functions and Random Matrix Theory.
Brown University (10/6/06).
See pdf
for a more extensive version.
Baseball Talks
- The Pythagorean Won-Loss Formula in Baseball (An
Introduction to Statistics and Modeling) (60 minute version)
Brown University (9/28/05) and (12/7/05):
slides(tab)
slide(no tab)
paper_pdf. Shorter 15 minute version: 2006 Hudson River
Undergraduate Mathematics Conference (4/8/06):
slides(tab)
slides(no tab)
-
The Pythagorean Won-Loss Formula in Baseball: An
Introduction to Statistics and Modeling (20 minute version):
Society For American Baseball Research, Boston
Meeting, Boston, MA (5/20/06):
slides(tab)
slides(no
tab)
paper_pdf. Williams
College (40 minute version, 1/15/08):
pdf.
Holy Cross (50 minute version, 2/7/08):
pdf. Western New England
College (40 minute version, 1/15/08):
pdf. Connecticut Smoky Joe Wood SABR Chapter, Hamden, CT (30 minute version,
2/16/08)
pdf.
-
See also talks on Computers and Mathematics Education.
- COURSES:
Spring '08:
Math 197,
Math 162.
Spring '09 (at Williams):
Math 406.
- Some previous course webpages:
Math 35 (honors
multivariable calculus),
Math 54 (honors linear algebra),
Math 153 (abstract
algebra).
-
MATH LINKS:
Arxiv
MathSciNet
Mathlabs (Princeton
, NYU,
OSU,
AIM)
Brown Math
Dept
Brown Seminars
Brown
Math DUG
Williams Math Dept
PERSONAL LINKS:
Personal Homepage
photos of Cam
photos of Brown
Pictures
My Twistie Art
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