My Talks


I will be giving two talks at the MOVES conference in August 2013.

I am available to give many different talks. These are my talks that I already gave somewhere and can resurrect and give them again upon request:

My talks can be adjusted for different audiences. If you would like to schedule me to speak to your group or to arrange a math party, please email me.


Secrets of Great Presentations

I gave this talk in July 2012 and July 2013 for RSI, and in April 2013 for PRIMES.


How Not to Write and How to Write a Math Paper

I give this talk every year for RSI students.

Abstract

I will show you my collection of bad mathematical writing. I will also discuss most common mistakes of RSI students. In addition, I will explain how to write a good math paper. The talk is targeted for students who never or almost never wrote a math paper. The goal is to prevent you from making mistakes most first-time math writers make, thus saving yours and your mentor's time. Time permitting, I might even explain how to read a math paper.


Conway's Sequences

I gave this talk at MIT UMA on November 27, 2012.

Abstract

I will describe some sequences invented by John H. Conway.


MIT Mystery Hunt

I gave this talk at the celebration of the mind event on November 6, 2012.

Abstract

We will solve a puzzle from last year's MIT mystery hunt.


Manhole Covers and Convex Geometry

I gave this talk at MIT IAP on January 27, 2012; at the University of Michigan on Feb 3, 2012; at Penn State on Sep 6, 2012; at MAA-NES meeting on November 16, 2012; at Smith College on October 24, 2013.

Abstract

Why are manhole covers round? Bring your answer to this famous interview question. We will use manhole covers as a starting point to discuss some modern research in convex geometry.


Tricky Arithmetics

I gave this short talk for Martin Gardner Celebration of Mind on October 21, 2011 and at G4GX in March 2012.


Jewish Problems

I gave this talk to MIT UMA on October 18, 2011.

Abstract

I will explain how mathematics was used to discriminate against Jewish people at the entrance exams to the math department of Moscow State University thirty years ago. Many problems had a simple solution that was difficult to find. Such problems protected the administration from extra complaints and appeals.

I will give an historical background and discuss a lot of tricky problems that were referred to as "Jewish" or "Coffin" problems. If you want to prepare for my talk, try to formulate in two words the main idea behind a simple solution to the following problem:

Find all functions F(x) such that for any x1 and x2 the following inequality holds: F(x1) - F(x2) ≤ (x1 - x2)2.

In the second part of the lecture we will examine certain statistical studies to expose the fallacies in their conclusions. Once you practice analyzing several examples, you will never look at statistics the same way again.


Tricky Problems in Probability and Statistics

This talk can be adjusted to high school students and undergraduate students. I gave this talk at MIT IAP on January 28, 2011.

Abstract

We will discuss several famous problems in probability including the Monty Hall problem and the Two Children problem (with variations). These problems created turmoil among mathematicians, for it took some time for them to agree on their solutions.

In the second part of the lecture we will examine certain statistical studies to expose the fallacies in their conclusions. Once you practice analyzing several examples, you will never look at statistics the same way again.


Integers and Sequences

This talk is targeted for undergraduate math students or advanced high school students. I assume the knowledge of binomial coefficients. I gave variations of this talk at BAE Systems, The Math Circle, UMA MIT, IAP MIT, Harvard Math Table, Princeton University Math Club, Girls' Angle, G4G8 (a short version), Wayne State University, Metroplex Math Circle, Shevah-Mofet, Tel-Aviv, ITA Software, UMass Lowell, WaM program at IAS 2010.

Abstract

Have you ever heard of "untouchable numbers"? How about "aspiring numbers"? I will tell you what they are.

I will explain how "perfect numbers" are connected to Mersenne primes. I will describe the biggest known prime number.

Have you ever wondered which is the most famous number sequence? Or which is the most versatile sequence? We will discuss that.

What is the largest amount of money in coins that you can have without being able to make change for a dollar? You can bring your answer to this seminar. What is so special about 1089? You will learn that, too. Is 42 (The Answer to Life, the Universe, and Everything) more famous than 47 (the secret Star Trek TNG number)? I promise you the answer to that.

I will also show you key Internet resources about numbers, so that you'll be able to discover new truths about your favorite numbers.


Baron Munchhausen's sequence, (joint work with Konstantin Knop and Alexey Radul)

This talk can be adjusted to high school students and undergraduate students. I gave this talk at UMA MIT 2010, IAP MIT 2010 (a short version), WaM program at IAS 2010.

Abstract

The Baron Munchhausen's coin problem appeared in a Russian Olympiad. We created a sequence out of this problem. I will completely describe the sequence. On the way, I will talk about decompositions of integers into triangular numbers and touch upon the Riemann hypothesis.


Modern Coin-Weighing Puzzles

This talk can be adjusted to high school students and undergraduate students. I gave this talk at MIT's Women in Mathematics Series in October 2010.

Abstract

I will discuss several coin-weighing puzzles and related research. Here are two examples of such puzzles:

1. Among 10 given coins, some may be real and some may be fake. All real coins weigh the same. All fake coins weigh the same, but have a different weight than real coins. Can you prove or disprove that all ten coins weigh the same in three weighings on a balance scale?
2. Among 100 given coins, four are fake. All real coins weigh the same. All fake coins weigh the same, but they are lighter than real coins. Can you find at least one real coin in two weighings on a balance scale?

You are not expected to come to my talk with the solutions to the above puzzles, but you should have thought about how to find the only fake coin that is lighter among many real coins in the minimum number of weighings.


Invariants

This talk is targeted for people who are interested in problem solving. I gave this talk at UMass, Lowell, Girls' Angle and MIT's Putnam Problem Solving class (many times), Idea Math in 2010, Math Circle at State College.

Abstract

Invariants can produce beautiful solutions to many Olympiad style problems. I show two magic tricks during my talk.


PRIMES

This talk is targeted for people who are interested in joining the PRIMES at MIT. I gave this talk at HMNT and Splash in the fall of 2010.

Abstract

I will describe how PRIMES work and give examples of research projects for high school students.


Set Game Theory

This talk is targeted for high school students or any people who love the game of set. I gave this talk at The Math Circle, the program for Women and Mathematics in Princeton 2009, PRIMES-Circles in 2013.

Abstract

It is not set theory. It is not game theory. It is the theory of the game of set. I will teach you how to play the game, explain the game's theory and then show some bonus activities. I have only four sets of the game of set. If you have a set of the game, please bring it along.


Clifford Algebras and Graphs

This talk is targeted for undergraduate and graduate students. I gave this talk at MIT combinatorics seminar, Hebrew University, Bar-Ilan University, Brandeis.

Abstract

I will show how to associate a Clifford algebra to a graph. I will describe the structure of these Clifford graph algebras, with the help of a variety of examples and pictures. You'll learn which graphs correspond to isomorphic Clifford algebras and hear about other related sets of graphs. I'll even hint at how this construction can be used to build models of representations of simply-laced compact Lie groups.


Binary Numbers

This talk is targeted for middle-school children. I gave this talk at The Math Circle, Girls Angle, Metroplex Math Circle, MetroWest School of Mathematics, PRIMES-Circles in 2013.

Abstract

I'll teach binary numbers, show two magic tricks and then we'll play with binary dollars.


Divisibility

This talk is targeted for middle-school children. I gave this talk at MetroWest School of Mathematics.

Abstract

I will discuss the divisibility rules, teach you to play the flip-flop game and dazzle you with two magic tricks.


Topology and Art

This talk can be adjusted to different levels from middle-school to graduate school. I gave this talk at the program for Women and Mathematics in Princeton 2008, at MIT Splash 2011 and MIT IAP 2012.

Abstract

I'll use drawings of Anatoly Fomenko and YouTube movies to discuss topology.


Unique Tournaments and Radar Tracking

This talk is targeted for undergraduate or graduate math students. I gave this talk at MIT Combinatorics seminar, Tel-Aviv University Combinatorics seminar,

Abstract

I will talk about radar tracking rules and define tracking and non-tracking sequences. I will also discuss tournaments, score vectors and define unique tournaments. One of the non-tracking sequences is the same as the sequence counting unique tournaments. I will define a bijection between unique tournaments and binary strings.


Lottery Mathematics

This talk is targeted for a general audience. I gave this talk at BAE Systems, The Math Circle, UMA MIT, IAP MIT, Brandeis, 2011 MIT Open House.

Abstract

If you analize the Mega Millions lottery game, the probability of winning and the expected value of the game depend on the Jackpot. How big should the Jackpot be in order that your expected return is bigger than your investment? Is Mega Millions ever worth playing?

Do you know how your chances change when you buy many tickets or when you pool money together with other people?

We'll look at other lotteries and learn about famous scams, as well as some clever, not-so-famous schemes for attempting to beat lotteries.


Double Trouble

This talk is targeted for curious programmers and advanced computer science students. Here are the PowerPoint slides of my Double Trouble talk. If you prefer to think about puzzles before reading their solutions, then watch this presentation as a slide show. I gave this talk at MIT.

Abstract

I have a large collection of the puzzling behaviors of Doubles in Java. First I'll explain the theory behind the doubles, and then I'll offer suggestions on how to handle the double's misbehavior and what to avoid. Doubles might be scary, but they are also fun.


Pi Day

This half-hour talk is targeted for a general audience of math lovers. I gave this talk at BAE Systems. PowerPoint Pi Day Talk Slides

Abstract

In a celebration of the Pi Day I will share with you fun facts about number Pi.


Math Party

This party is targeted for a general audience of math lovers starting from age 12. They are arranged in teams of at least four people and the fastest team wins. I conducted such a party at BAE systems and at the Program for Women and Mathematics in Princeton in 2008, WaM program at IAS 2010, 2011 WaM program at IAS.

Abstract

I you will compete in fun hands-on math activities.


Modern Cryptography

This talk is targeted for non-mathematicians or beginner mathematicians interested in modern cryptography. I gave this talk at BAE Systems.

Abstract

Starting from classical cryptography and continuing into public-key cryptography, I discuss different aspects of modern cryptography.


The Odd One Out

This ten-minutes talk is targeted for a general audience. I gave this talk at G4G9.

Abstract

I have odd-one-out questions, that why I invented one.


Unrevealing Coin Weighings

A ten-minute talk for puzzle lovers. I gave this talk at G4G9.

Abstract

A coin weighing puzzle that first appeared at a Russian Olympiad has roots in cryptography.


Last revised April 2010