Geometry, Combinatorics, Patterns and Fun
Speaker: Niraj Khare, Faculty Candidate for CMU Qatar 
Time: 5:00pm on Wednesday, Mar.23rd, 2016 
Location: DH 2315 
Abstract: Click here for a pdf version 
Talk Slides: slides in pdf version 
Trigonometry Revisited or: If Fourier Had a Quantum Computer
Speaker: Zijian Diao, Faculty Candidate for CMU Qatar 
Time: 5:00pm on Wednesday, March 2nd, 2016 
Location: DH 2315 
Abstract:
Is sine of 1 degree rational? At a glance this question seems light years away from quantum computing, a cuttingedge research area where computer science meets quantum mechanics. Surprisingly, this question matters not only in the mathematical world, but also in the quantum realm. Its answer and many other rudimentary facts of trigonometry have found their way into the study of various research problems in quantum computing. In this talk we will explore these intriguing connections through the interplay of quantum algorithms and topics from number theory and classical analysis. Along the way, we will solve a longstanding puzzle in quantum search and provide a quantum approach to the centuriesold Basel problem.

Thue Theorems and Avoidable Patterns
Speaker: Martin Juras, Faculty Candidate for CMU Qatar 
Time: 5:00pm on Wednesday, Feb.24th, 2016 
Location: WEH 8220 
Abstract: Click here for a pdf version 
Infinite Dimension in Linear Algebra: A Case for Functional Analysis
Speaker: Adrian Hagerty, PhD student in Math Dept at CMU 
Time: 5:30pm on Wednesday, Feb.17th, 2016 
Location: DH 2315 
Abstract: The study of Functional Analysis forms an important role in the modern fields of PDEs and Calculus of Variations. This involves taking the familiar notion of a vector space and bringing it to the realm of infinite dimensions. What new problems arise as we attempt to generalize our old tools to the infinite setting? 
What is Structure?
Speaker: Clive Newstead, PhD student in Math Dept at CMU 
Time: 5:30pm on Wednesday, Jan.27th, 2016 
Location: DH 2315 
Abstract:
The idea of equipping a set with a structure is ubiquitous in mathematics. For example, graphs are sets equipped with an edge relation, groups are sets equipped with an algebraic structure, topological spaces are sets equipped with a notion of openness, posets are sets equipped with a notion of order... the list goes on forever and ever and ever. This talk will introduce a candidate for defining 'structure' in the abstract. With the tools we develop, we can prove some pretty cool stuff in enumerative combinatorics. 
Probability and Intuition
Speaker: Peter Winkler, William Morrill Professor of Mathematics and Computer Science, Dartmouth 
Time: 5:30pm on Wednesday, Dec.2nd, 2015 
Location: DH 1112 
Abstract:
Supposedly our intuition about probabilityeven though humans invented the conceptis faulty. Lots of puzzles, naturally, are designed to lead us down the garden path to incorrect conclusions. But maybe our intuition is not as bad as we think. We'll take a fresh look at some paradoxes, old and new, to see whether we or our assumptions are at fault.

Poster: Poster

Fine Structure in Shapememory Alloys
Speaker: Winston Yin, senior at CMU, math and physics double major 
Time: 5:30pm on Wednesday, Nov.18th, 2015 
Location: PH 100 
Abstract:
The peculiar properties of a shapememory alloy are the result of the fine structure formed between its several crystalline forms. How do these fine structures arise from basic ideas about a crystal? In this talk, I will explain how infinitely fine structures are a natural consequence of integral minimization problems, as well as the project I worked on at Oxford this summer.

Variational Problems in Materials Science and Image Inpainting
Speaker: Irene Fonseca, Mellon College of Science University Professor of Mathematics,
Director of Center for Nonlinear Analysis

Time: 5:30pm on Wednesday, Nov.11th, 2015 
Location: PH 100 
Abstract: A plethora of physical and technological applications ranging from analyzing instabilities in materials science to image analysis in computer vision are subject to rigorous mathematical understanding through recently developed methods and articulation of ideas in the calculus of variations, geometric measure theory, and nonlinear partial differential equations. In this talk, these techniques will be used for recolorization of damaged images.

The Projective Heat Map
Speaker: Richard Schwartz, Chancellor`s Professor of Mathematics, Brown University

Time: 11:30 on Friday, Oct.16th, 2015 
Location: WEH 8200 
Abstract: Abstract and Slides

MeetandGreet with Paul Raff
Triples
Speaker: PoShen Loh, Math Professor at CMU, USA IMO Lead Coach

Time: 5:30 on Wednesday, Sept.30th, 2015 
Location: PH 100 
What's the longest sequence of triples (x1, y1, z1), (x2, y2, z2), ... that satisfies the following properties?
(1) Each number is an integer between 1 and N inclusive.
(2) For every j less than k, if we compare the triples (x_j, y_j, z_j) and (x_k, y_k, z_k), there are at least two coordinates in which the latter triple strictly exceeds the former triple.
It turns out that this simplesounding problem is equivalent to a question from Ramsey Theory, inspired by a question from kmajority tournaments, and related to deep question involving induced matchings and Szemeredi' s Regularity Lemma.
The talk will be a tour of Combinatorics which introduces many of these concepts along the way.
Sticky Particles
Speaker: Adam Williams, senior math major at
CMU 
Time: 5:30 on Wednesday, Apr 29th, 2015 
Location: Scaife 125 
Imagine you have a finite set of particles, moving along the x axis, with
fixed masses and initial velocities. When two particles collide, they
*stick* together to form a new particle, preserving the mass and momentum
of the original two. This is a simple setup, but seems potentially
difficult to work with mathematically. Adam shows you how you can use math
to study this system in a way that makes it much more understandable.
Unexpected distribution phenomenon resulting from Cantor
series expansions
Speaker: William Mance, PhD, CMU alumnus 
Time: 5:00 on Wednesday, Apr 22nd, 2015 
Location: Scaife 125 
We explore in depth the theoretic and statistical properties of
certain sets of numbers arising from their Cantor series expansions.
As a direct consequence of our main theorem we deduce numerous new
results as well as strengthen known ones. This work was coauthored
with Dylan Airey while he was still a high school student at the
Texas Academy of Mathematics and Science. Our main theorem
will touch on issues related to computability theory, ergodic theory,
fractal geometry, number theory, and probability theory.
Why the IRD cares about the Riemann Zeta Function and Number Theory
Speaker: Steven Miller, Professor at Williams
College 
Time: 5:30 on Wednesday, Mar 25th, 2015 
Location: Scaife 125 
Many systems exhibit a digit bias. For example, the first digit
base 10 of the Fibonacci numbers or of 2^n equals 1 about 30% of
the time; the IRS uses this digit bias to detect fraudulent corporate tax
returns.
This phenomenon, known as Benford s Law, was first noticed by
observing which pages of log tables were most worn from age – it is a good
thing there were no calculators 100 years ago! We will discuss the general
theory and application, talk about some fun examples (ranging from the 3x1
problem to the Riemann zeta function), and if time permits discuss
some joint results with my REU students.
The Birch and SwinnertonDyer conjecture
Speaker: Tomer Reiter, senior math major at CMU 
Time: 5:30 on Wednesday, Mar 4th, 2015 
Location: Scaife 125 
The Birch and SwinnertonDyer conjecture is one of the Millennium
Problems. The conjecture relates the group of rational points on an
elliptic curve to information associated with the equation for the
elliptic curve over finite fields.
In the talk, we will see some of setup for the conjecture, the
statement and some of the partial progress made. I will basically
assume David's talk last time as a prerequisite, but I will briefly
go over the facts about elliptic curves he mentioned that we will
need.
The Congruent Number Problem and Elliptic Curves
Speaker: David Mehrle, senior math major at CMU 
Time: 5:30 on Wednesday, Feb 18th, 2015 
Location: Scaife 125 
A positive integer N is called congruent if it is the area of a
right triangle whose sides have rational lengths. Determining
whether or not a given positive integer is congruent is a
millenniaold problem that is still open today. I will explore this
problem and several attempted solutions, including an interesting
modern approach using elliptic curves.
Missing the Point
Speaker: Misha Lavrov, PhD student at CMU 
Time: 5:30 on Wednesday, Jan 28th, 2015 
Location: Scaife 125 
If you are speaking with an alien from Mars who knows a lot of
math and has never heard the word Euclid, explaining what
geometry is can be frustrating. You will try very hard to come up
with foolproof ways to axiomatize geometry, and the alien will
persist in coming up with bizarre structures that look nothing
like what you imagined.
In 1899, Hilbert came up with a set of 16 alienproof axioms for
plane geometry. (That is not quite true. He had 17. But there’s
been some progress in the intervening century.) In this talk, I
will play the role of the alien in an effort to persuade you that
the task of Hilbert was not an easy one.
Special Guest Speaker
Speaker: Noam Elkies, Professor of Mathematics, Harvard University

Time: 5:30 to 6:30 on Wednesday, December 3rd

Location: WEH 7500

TBA
The fundamental theorem of algebra
Speaker: Giovanni Leoni, Professor of Mathematics 
Time: 5:30 to 6:30 on Wednesday, October 27th

Location: DH 1112

In this talk we will discuss the fundamental theorem of algebra and give an analytical proof.
You do not have to believe in transcendental numbers
Speaker: Boris Bukh, Assistant Professor of Mathematics 
Time: 5:30 to 6:30 on Wednesday, October 8th

Location: DH 1112

The transcendental numbers are the atoms of the number line  they are everywhere, but few have seen one. No longer you will have to believe in the existence of these halfmythical numbers! I will arm you with the knowledge that will enable you to write a number down, and prove to your cat that it is transcendental!
Pizza will be served.
When IMO meets Research
Speaker: Po Shen Loh, Assistant Professor of Mathematics 
Time: 5:30 to 6:30 on Wednesday, September 24th

Location: MM 103

This year, problem 6 on the International Math Olympiad turned out to be a
semiopen research problem. The originally proposed problem is solvable
using basic methods, but it is still open to determine the best possible
result. A set of lines in the plane is in general position if no two are
parallel and no three are concurrent. A set of lines in general position
cuts the plane into cells, some of which have finite area; we call these
finite cells. Prove that for all sufficiently large $n$, in any set of $n$
lines in general position it is possible to color at least $\sqrt{n}$ of
the lines blue in such a way that none of its finite cells has a completely
blue boundary. What's the best bound that you can get? We'll improve the
stated bound using techniques from probabilistic combinatorics and extremal
hypergraph theory.
Assessing Artifacts: Using Calculus of Variations to Segment Damaged Images
Speaker: Nick Takaki, Undergraduate 
Time: 5:30 to 6:30 on Wednesday, September 10th 
Location: DH 1112

A biphase approximation of an image is a twocolor piecewiseconstant approximation of the original image which maximizes regional fidelity while minimizing complicated boundaries. When it comes to segmenting images, human intuition is very strong. We often have strong gut feelings about which pixels belong in which regions, where object boundaries should be, and what should be discounted as noise or damage. Variational image segmentation seeks to formalize these "gut feelings" by creating a functional which quantifies the error of approximation, and then defining correct segmentations as local minima of this functional. In this talk, I will discuss the intuition behind variational image approaches, popular regionbased segmentation methods including the ChanVese model, and my group's summer research into a segmentation method which dynamically identifies artifacts and corrects shadows.
Chaos In Cellular Automata
Speaker: Carson Sestili, Undergraduate 
Time: 5:30 on Thursday, May 1, 2014 
Location: WEH 5415 
An elementary cellular automaton is a sort of computational model. States are sequences of bits. Transitions between states are specified by a simple, deterministic rule that updates each bit according to a small neighborhood around that bit in the previous state. Even though the model is simple to describe, many cellular automata have surprisingly beautiful and complicated behavior. In some cases their behavior is so unpredictable that it might be called "random," even though there is no randomness in the system. In this talk I will show why several automata exhibit chaotic behavior, for a popular definition of chaos.
The Estimathon
Speaker: Andy Niedermaier, Jane Street Capital

Time: 5:30pm on Wednesday, March 26, 2014

Location: DH 2210

They're called Fermi problems...
 how many traffic lights are there in Boston?
 how many social security numbers are primes?
 how many calories are in an average Cheesecake Factory?
 how many times will this activity get rescheduled due to bad weather?
Jane Street presents "The Estimathon." Attempt 13 estimation problems in 30 minutes, ranging from totally trivial to positively Putnamesque. Work in teams to come up with the best set of confidence intervals. Compete against your fellow students for fame* and fortune^!
(* fame is subjective)
(^ there will be prizes for the winners)
How Physics can help with the "Big Picture" in Math
Speaker: Ira Rothstein, Professor of Physics 
Time: 5:30 on Wednesday, February 19, 2014 
Location: DH 2315 
Why are differential equations so ubiquitous? It seems that all
physical systems are described by a set of differential equations.
Perhaps we should stop and ask why? In this talk I will explain
how a certain set of fundamental principle that apply to all physical
systems automatically lead to differential equations (DE's) as equations of
motion, as opposed to say integral equations. I will also discuss how
the symmetries of physical systems, and their corresponding DE's,
naturally lead to solutions via the use of group theory. Finally I will
discuss how the principle of observer independence leads to the
idea of differential geometry.