The seminar's main goal is to expose culturally ambitious participants to some mathematical notions not taught in standard courses. These topics form an important part of mathematical folklore, and may prove useful for doing research and enhancing teaching. Lectures will be given mostly by graduate and undergraduate student participants.

The current years talks can be found at What is ...? Seminar talks.

## Previous What is ...? talks

2022 | 2021 | 2019 | 2018 | 2017 | 2016 | 2015 | 2014 | 2013 | 2012 | 2011 | 2010 | 2009

### 2022 Talks

- Thu June 23: Linus Ge, What is the Erdős Distinct Differences Problem?
- Tue June 28: Sachin Gautam, What is the Perron—Frobenius Theorem?
- Thu June 30: Bhawesh Mishra, What is a Multidimensional Continued Fraction?
- Tue July 5: Mario Gomez Flores, What is Ptolemy's Inequality?
- Thu July 7: Dennis Sweeny, What is the Riesz Rearrangement Inequality?
- Tue July 12: Mikey Reilly, What is Amenability?
- Thu July 14: Ahn Lee, What is the Erdős Discrepancy Problem?
- Tue July 19: Jake Huryn, What is a Generalized Bernoulli Number?
- Thu July 21: Kabir Belgikar, What is Combinatorial Nullstellensatz?
- Tue July 26: Vilas Winstein, What is a Ramanujan Graph?

### 2021 Talks

- Tue June 8: Nick Bolle, What is Singular Value Decomposition?
- Thu June 10: Sachin Gautam, What is Poncelet's Porism?
- Tue June 15: Bhawest Mishra, What is the Collatz Conjecture?
- Thu June 17: Jesse He, What is Arrow's Impossibility Theorem?
- Tue June 22: Vilas Winstein, What is the Limit of a Sequence of Graphs?
- Thu June 24: Sohail Farhangi, What is the Lovász Conjecture on Hamiltonian Cycles?
- Tue June 29: Torey Hilbert, What is Bayesian Decision Theory?
- Thu July 1: Mikey Reilly, What is Minkowski's Question Mark Function?
- Tue July 6: John White, What is the Alexander Horned Sphere?
- Thu July 8: Dong-june Choi, What is a Besicovitch Set?
- Tue July 13: Ethan Ackelsberg, What are the Euler—Lagrange Equations?
- Thu July 15: Joseph Paugh, What is an Appolonian Gasket?
- Tue July 20: Amanda Pan, What are Surreal Numbers?

### 2019 Talks

- Tue June 25: Boris Mityagin, What is a Sylvester Matrix?
- Thu June 27: Jake Huryn, What is the Grigorchuk Group?
- Tue July 2: Michael Lane, What is a Markoff Number?
- Tue July 9: Nik Henderson, What is the Rado Graph?
- Thu July 11: Ethan Ackelsberg, What is Shannon Entropy?
- Tue July 16: Enrique Gomez, What is the Rental Harmony Theorem?
- Thu July 18: Vilas Winstein, What is Shor's Algorithm?
- Tue July 23: Dennis Sweeney, What is the Isoperimetric Inequality?
- Thu July 25: Mario Gomez, What is Nash Equilibrium?
- Tue July 30: James Enouen, What is the Perfect Shuffle?

### 2018 Talks

- Tue June 12: Andreu Ferre-Moragues, What is the Müntz-Szász Theorem? [pdf]
- Thu June 14: Will Hoffer, What is the Yang-Baxter Equation? [pdf]
- Tue June 19: Sohail Farhangi, What is the Continued Fraction Factoring Method? [pdf]
- Thu June 21: Vilas Winstein, What is the Recursion Theorem? [pdf]
- Tue June 26: Austin Antoniou, What is the Davenport Constant? [pdf]
- Thu June 28: Desmond Coles, What is Moonshine? [pdf]
- Tue July 3: James Enouen, What is the Markov and Lagrange Spectra? [pdf]
- Thu July 5: Megan Fava, What is Game Theory? [pdf]
- Tue July 10: Jake Huryn, What is FRACTRAN? [pdf]
- Thu July 12: Ishann Shah, What is Quantum Mechanics? [pdf]
- Tue July 17: Alex Beckwith, What is the Erdős–Kac theorem? [pdf]
- Thu July 19: Ethan Ackelsberg, What is the Arcsine Law? [pdf]
- Tue July 24: Josiah Oh, What is the Toeplitz Conjecture? [pdf]
- Thu July 26: Peter Huston, What is the Perron-Frobenius theorem? [pdf]

### 2017 Talks

- Tue June 20: Caleb Dilsavor, What is Luroth Expansion? [pdf]
- Thu June 22: Maxwell Budd, What are Rademacher Functions? [pdf]
- Tue June 27: Nik Henderson, What is a Weierstrass Point? [pdf]
- Thu June 29: Aidan Howells, What are Cassini Ovals? [pdf]
- Thu July 6: Sohail Farhangi, What is an Engel series? [pdf]
- Tue July 11: Dan Brogan, What is an Attractor? [pdf]
- Thu July 13: Joshua Yee, What is Topological Entropy? [pdf]
- Tue July 18: Miles Calabresi, What is Crofton's Formula? [pdf]
- Thu July 20, Vilas Winstein, What is the Lambda Calculus? [pdf]
- Tue July 25, Joseph Vandehey, What is the Hot Spot Theorem? [pdf]

### 2016 Talks

- Thu June 16: Carl Ahlborg, What is Orientation?
- Tue June 21: Miles Calabresi, What is Elliptic Curve Cryptography? [pdf]
- Thu June 23: Daniel Glasscock, What is an elliptic integral addition formula? [pdf]
- Tue June 28: Andreu Ferre, What is Monsky's Theorem? [pdf]
- Thu June 30: Anthony Ciavarella, What is Q Deformed Calculus? [pdf]
- Tue July 5: Josh Yee, What is Chaotic Behavior in Iterated Function Systems?
- Thu July 7: Charles Baker, What is von Neumann's Minimax Theorem?
- Tue July 12: Nik Henderson, What is Zeckendorf's Theorem? [pdf]
- Thu July 14: Aidan Howells, What is Riemann Integration? [pdf]
- Tue July 19: George Hauser, What is the Erdos Distinct Distances Problem?
- Thu July 21: Nick Hemleben, What is the real projective space?
- Tue July 26: Simon Zhang, What is the Veronese map? [pdf]
- Thu July 28: Michael Crawshaw

### 2015

- Thu June 18: Daniel Glasscock,
*What is the Kakeya needle problem?*[pdf] - Tue June 23: Mike Steward,
*What are Integer-Valued Polynomials?*[pdf] - Thu June 25: Gabriel Khan,
*What is the Ricci Flow?*[pdf] - Tue June 30: Boming Jia,
*What is the Denjoy Integral?*[pdf] - Tue July 7: Nick Hemleben,
*What is the Four Color Theorem?*[pdf] - Thurs July 9: Carl Ahlborg,
*What are Kissing Circles?*[pdf] - Tue July 14: Ricky Magner,
*What is Liouville's Theorem on Integration?*[pdf] - Thu July 16: Allison Paul & Sandeep Silwal,
*What is Waring's Problem?*[pdf] - Tue July 21: Ji Hoon Chun,
*What is the Busemann-Petty Problem?*[pdf] - Thu July 23: Shenhui Liu,
*What are Kloosterman Sums?*[pdf]

### 2014

- Thu June 19: Charles Baker,
*What are Ceva's and Menelaus's Theorems?*[pdf] - Tue June 24; Joel Moreira,
*What is a RIP Matrix?*[pdf] - Thu June 26: Boming Jia,
*What are Kepler's Laws?*[pdf] - Tue July 1: Duncan Clark,
*What is Kuratowski's 14 set theorem?*[pdf] - Thu July 3: Florian Richter,
*What are mathematical games and the Hales-Jewett Theorem?* - Tue July 8: Anthony Ciavarella,
*What is a Fresnel integral?*[pdf] - Thu July 10: Donald Robertson,
*What is hyperbolic geometry?*[pdf] - Tue July 15: Ricky Magner,
*What is the Ax-Grothendieck Theorem?*[pdf] - Thu July 17: Ji Hoon Chun,
*What is tetration?*[pdf] - Tue July 22: Daniel Glasscock,
*What is the crank of a partition?*[pdf] - Thu July 24: Andrzej Derdzinski,
*What is Newton vs. Kepler, again?*[pdf]

### 2013

- Thursday, June 20: Daniel Glasscock,
*What is graphon?*[pdf] - Tuesday, June 25: Angelo Nasca,
*What is Birkhoff universality?*[pdf] - Thursday June 27: Charles Baker,
*What is Crofton formula?*[pdf] - Tuesday, July 2: Rudy Perkins,
*What is log algebraicity?*[pdf] - Tuesday, July 9: John Johnson,
*What is ultrafilter?*[pdf] - Thursday, July 11: Davis Buenger,
*What is Bernoulli numbers?*[pdf] - Tuesday, July 16: Florian Richter,
*What is the word problem for groups?* - Thursday, July 18 at 3:15: Andrew Krieger,
*What is inversive geometry?*[pdf]

and at 3:45: Ben O'Connor,*What is the Bellows Conjecture?*[pdf] - Tuesday, July 23: Younghwan Son,
*What is a quasicrystal?*[pdf] - Thursday, July 25 at 3:15: Gabe Khan,
*What is Noether's theorem?*[pdf]

and at 3:55: Ji Hoon Chun,*What is a sphere packing?*[pdf]

### 2012

- Thu, June 21: Daniel Glasscock,
*What is a braid group?*[pdf] - Tue, June 26: Tae Eun Kim,
*What is Plateau's problem?*[pdf] - Thu, June 28: Kevin Yuh,
*What is quantum computing?*[pdf] - Tue, July 3: Isaac Smith,
*What is Euler's prime generating polynomial?*[pdf] - Thu, July 5: Charles Baker,
*What is Morley's miracle?*[pdf] - Tue, July 10: Andrew Krieger,
*What is Ulam's game?*[pdf] - Thu, July 12: Paul Apisa,
*What is Weyl's law?* - Tue, July 17: John Michel,
*What are folk theorems of game theory?* - Thu, July 19; Ben O'Connor,
*What are iterated function systems?*[pdf] - Tue, July 24; Joel Moreira,
*What is an intrinsically knotted graph?*[pdf] - Thu, July 26; Ji Hoon Chun,
*What is the Hausdorff dimension?*[pdf] - Tue, July 31; Michael Steward,
*What is Napoleon's theorem?*[pdf] - Thu, August 2: Yanli Wang,
*What is the logistic model?*[pdf]

### 2011

- Wed, June 22: Daniel Shapiro,
*What is building new triangles from old?*[pdf] - Mon, June 27: Rudy Perkins,
*What are factorials in function fields*? - Wed, July 6: Jonathan Michel,
*What is a Moufang Loop?* - Mon, July 11: Keith Stephens,
*What are PV numbers and Salem numbers?*[pdf] - Mon, July 18: Daniel Grollmus,
*What is a generalized trigonometric function?* - Mon, July 25: Michael Walker,
*What is Benford's law?*[pdf] - Mon, August 1: Ji Hoon Chun
*,What are Egyptian fractions?*[pdf] - Mon, August 8: Patrick Schnell,
*What are Pfaffians and perfect matching?*[pdf] - Mon, August 15: Charles Baker,
*What**is the Jones Polynomial?*

### 2010

- Thursday, June 24: Charles Baker,
*What is a Turing Machine?*[pdf] - Monday, June 28: Donald Robertson
*,**What is Desargue's theorem?*[pdf] - Thursday, July 1: Andy Nicol
*,What is a Cayley graph?*[pdf] - Thursday, July 8: Jeff Lindquist
*, What is a Ford Circle?*

Ford Circles provide a method of embedding the rational numbers into the Euclidean plane R^2. We will describe this embedding and use it to prove some facts related to Farey Series and Diophantine Approximation, most notably Hurwitz's theorem. - Monday, July 12: Rob Bradford,
*What is Zariski Topology*?

In algebraic geometry, the Zariski topology defines the basic structure of varieties and schemes. We will define this topology, discuss some of its basic properties, and give examples of its applications in algebraic geometry. - Thursday, July 15: Brittany Albrinck:
*What is Phyllotaxis?*[pdf]

Math surrounds us in our everyday lives, even in nature. When a normal human being looks at a sunflower they see beauty. But why is it so beautiful? One could argue it is because Fibonacci numbers are hidden within its seeds and create an aesthetically pleasing pattern. Math can be found in the arrangement of most plants and phyllotaxis is the study of these mathematical arrangements. Further information appears in Scott Hotton's thesis? [pdf] - Monday, July 19: Daniel Shapiro,
*What is the 1, 2, 4, 8, Theorem?*

In 1898, Hurwitz proved that a bilinear n-square identity exists only when n is 1, 2, 4, or 8. Consequently: If a real finite-dimensional algebra A has a multiplicative "norm" then dim A = 1, 2, 4 or 8. We will outline a proof and mention some generalizations. - Thursday, July 22; Jack Cheng,
*What is the Cook-Levin Theorem?* - Monday, July 26: Vitaly Bergelson,
*What is the Hindman's theorem (via ultrafilters)?* - Thursday, July 29: Daniel Poole
*, What is the Cauchy principal value?* - Monday, August 2: Theodore Dokos,
*What is squaring the square?* - Monday, August 9: Younghwan Son,
*What is the Duffin Schaeffer conjecture?*[pdf] - Thursday, August 12: Drew Meyer,
*What is Pick's theorem?* - Monday, August 16: Neal Edgren,
*What is Bieberbach's conjecture?* - Thursday, August 19: Ross Askanazi,
*What is the Perron-Frobenius theorem?*

### 2009

- Mon, June 29: Daniel Poole,
*What is a non-atomic finite measure?*[pdf] - Thu, July 2: Bill Mance,
*What are normal numbers and uniform distribution?*[pdf] - Mon, July 6: Jack Jeffries,
*What is billiards?*[pdf] - Thu, July 9: Corey Staten,
*What is a Bohr compactification?*[pdf] - Mon, July 13: AJ Nasca,
*What is a non-standard analysis?*[pdf] - Thu, July 16: Paul Apisa,
*What is a Scissors congruence?* - Mon, July 20: James Talamo,
*What is Huygens's principle?* - Thu, July 23: Donald Robertson,
*What is a Penrose tile?*[pdf] - Mon, July 27: Stephen Swihart,
*What is Feigenbaum's constant?* - Thu, July 30: Andrew Nicol,
*What is the ZigZag theorem?*[pdf] - Mon, Aug 3: Yishun Dong,
*What is Kakeya's needle problem?*[pdf] - Thu, Aug 6: Clark Butler,
*What is fractional calculus?*[pdf] - Mon, Aug 10; James Unger,
*What are Sangaku problems?*[pdf] - Thu, Aug 13: Theodore Dokos,
*What are surreal numbers and games?*[pdf] - Mon, Aug 17: Jeffrey Lindquist,
*What is Van Schooten's locus problem?*[pdf] - Thu, Aug 20: Trent Ohl,
*What is a Young tableaux?*

[pdf] - Some links on this page are to .pdf files. If you need these files in a more accessible format, please contact webmaster@math.osu.edu . PDF files require the use of Adobe Acrobat Reader software to open them. If you do not have Reader, you may use the following link to Adobe to download it for free at: Adobe Acrobat Reader.