Dan Loeb
Prepared Talks:
- Mathematics of Voting (General):
- I am a specialist in the mathematics of voting. One title "Voting Fairly" introduces the concept of a voting scheme and discusses its applications to various domains. Various notions of fairness are compared, and fair voting schemes on a small number of voters are enumerated. Another title "Voting Schemes and the Shape of Democracy" studies the effect of perturbations to a voting scheme. I can also speak about issues related to the November 2000 US Presidential general election and its aftermath.
- Euler's Formula (General)
- The speaker will lead the participants to discover the relationship between the number of walls, towers and regions in a walled city. Our conjectures will be refined as attempted proofs are confronted with counterexamples. Applications include enumerating the five possible platonic solids and determining the "optimal" arrangement of dimples on a golf ball.
- Farey Sequence (General)
- The Farey Sequence is a very simple construction. Start by writing the numbers 1 and 1. Then keep on writing the sum of adjacent numbers between the two numbers:
- 1 1
- 1 2 1
- 1 3 2 3 1
- 1 4 3 5 2 5 3 4 1
- Many questions immediately come to mind: What numbers appear? What is the biggest number on each line? The smallest? What numbers appear together? How many times does each number appear? Applications include number theory, continued fractions and fractals.
- Combinatorial Games (General)
- The game of Nim is very simple. Players take turns removing stones from one of several piles. The player who empties the last pile wins. The speaker will lead the class in the discovery of the strategy to this simple game with an elegant theory behind it. Given sufficient time we can see how every "impartial" game can be translated into a position in Nim. Thus, if we can win at Nim then we can win at quite a few games.
- Mathematical Finance (Advanced)
- We will cover two main ideas of modern finance: portfolio optimization and option valuation. Portfolio optimization means allocating a fixed investment fund among instruments (e.g., stocks) in order to maximize return and/or minimize risk; the techniques range from matrix algebra to quadratic programming. In option valuation, we will derive the Black-Scholes formula under naive assumptions and then show how the modern no-arbitrage theory allows us to apply it more generally. The presenter will draw on practical examples from his consulting work.
- Richman Games (General)
- Richman games will be discussed. In a Richman game, instead of alternating moves, people bid for the right to make the next move. (For example, try playing Tic-Tac-Toe that way...). One of the most simple Richman games can be thought of as trying to create a synthetic bet on the World Series as a whole from a bookie who only allows bets on individual games, or equivalently it can thought of as valuing a binary put on a stock with a discrete price model.
- Classical Game Theory (General)
- Cooperative Game Theory (General) Cooperative game theory will be discussed. As an example, consider the following example: Alice and Bill can each earn $10/hr on her own. Cathy can earn nothing on her own. Alice and Bill can earn $25/hr together, Alice and Cathy $20/hr together, Bill and Cathy $12/hr together. Altogether they can earn $35/hr. How can/should/will Alice, Bill and Cathy share the $35?
Contact Information:
- Institution: Susquehanna International Group, LLP
- e-Mail Address: daniel.loeb@verizon.net
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