Click on an event title to see the associated poster. This only has events from late 2018 onwards, for older events click on the old website tag. For a board member to create a new event click
here .
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Nathaniel Bannister
2021-4-29
What's an anagram for Banach-Tarski? Banach-Tarski Banach-Tarski! The Banach Tarski theorem is a result from 1924 asserting that, given any two subsets A and B of R^n with n>=3 which are bounded with nonempy interior, there is a way to decompose A into finitely many pieces which, through a combination of rotations, reflections and translations, can be reassembled to make B. Some particularly surprising examples include when A is a ball and B is two balls or B is a larger ball. We will outline a proof of this result and outline some recent results showing that, under certain conditions, the pieces can be made somewhat "nice," including decomposing a square into finitely many Borel pieces and translating them to make a circle.
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Clarice Pertel
2021-4-8
L.E.J. Brouwer’s intuitionism was a controversial departure from classical mathematics and has been embraced by physicists and computer scientists, but not by classical mathematicians. In the Nuprl proof development system, much research has been done using intuitionistic mathematics. I will discuss Brouwer’s free choice sequences, as well as introduce homotopy theory and type theory. Finally, I will discuss how Vladimir Voevodsky’s univalence axiom provides an interesting lens with which to reimagine the foundations of mathematics.
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Professor Dylan Thurston
2021-4-1
Dylan Thurston will be delivering this year's annual Kieval Lecture! The talk will be at 4:00pm on Zoom. More information is available here.
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Tik Chan
2021-3-25
The theory of singular integral operators is one of the great achievements in analysis of the past century. Beginning in the 1950s, Alberto Calderón and Antoni Zygmund began developing what is now known as Calderón-Zygmund theory, which is now one of the cornerstones of harmonic analysis, in order to understand these objects. Since then, singular integrals and the methods developed from their study have become powerful tools throughout analysis, even finding some applications in the sciences. In this talk, we will introduce the concept of singular integral operators in harmonic analysis with a focus on the Hilbert transform. In particular, the emphasis will be on the methods used to study these objects and the big picture ideas behind the proofs rather than the specific results or technical details. Knowledge of basic analysis is assumed and familiarity with Lp spaces will be helpful (but not required as we will review all the necessary properties).
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Ely Sandine
2021-2-22
In this talk we'll compute the Fourier transform of log |x| using linear algebra. We'll start by showing how to derive the important properties of the Fourier transform without resorting to integration by parts and then go from there. Some familiarity with log is assumed, although in principle not required. There will be pictures.
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Daniela Rodriguez-Chavez
2020-10-26
It is hypothesized that as a result of the buildup of greenhouse gases in the atmosphere, as early as within the next few centuries a sixth mass extinction will occur. Because the oceans absorb 30% of carbon (a greenhouse gas) emissions released into the atmosphere, they are key components in understanding both past and future climate events. In this talk, we will examine an oceanic carbon cycle model, and the implications of the results regarding a potential mass extinction.
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Andrew Graven
2020-10-12
Poincar\'e's Last Geometric Theorem states that if $T:A\rightarrow A$ is any any area-preserving homeomorphism of the annulus $A$ which ``twists'' the inner and outer boundaries of $A$ in opposite directions, then $T$ has at least two fixed points. Poincar\'e was originally interested in this result because it implies the existence of periodic orbits in the three body problem. He proved several special cases of the theorem via intuitive geometric arguments, however later complete proofs lost much of this geometric flavor. We extend Poincar\'e's argument to the general case of the theorem, while maintaining strong emphasis on his original geometric constructions. Joint work with Professor John Hubbard.
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Nikita Borisov
2020-09-28
Given a ring $R$, a map $\delta:R\rightarrow R$ is a derivation if it is additive and satisfies the Leibniz rule ($\delta(ab)=\delta(a)b+a\delta(b)$ for all $a,b\in R$). It is well known that the set of derivations on a ring, denoted $\text{Der}(R)$, form a Lie ring (i.e. $\text{Der}(R)$ is closed under addition and lie brackets $[\delta_1,\delta_2]=\delta_1\circ\delta_2-\delta_2\circ\delta_1$), but are typically not closed under composition. Take for instance the formal derivative on polynomials of $x$; the double derivative doesn't satisfy the Leibniz rule. We would like to study the cases when they are closed under composition (i.e. $\Der(R)$ forms a ring) with a particular focus on finite rings.
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John Kolesar
2020-03-18
Even though Euclid takes a systematic approach to his proofs in the \emph{Elements}, his proofs do not qualify as fully formal because they rely on a number of unstated assumptions about the nature of plane geometry. Modern mathematicians have sought to fill the gaps in Euclid's foundations for geometry by enumerating the necessary properties of the plane at the most basic possible level. The end result bears little resemblance to Euclid's original list of axioms but enables electronic proof assistants to work with plane geometry.
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Ryan Kannanaikal
2020-03-16
A mathematician, dog, and cow walk into a bar. The bartender says, "hey, no animals allowed!" The mathematician says, "wait up these animals are knot theorists." To which the bartender says, "I've known knot theorists who were animals, but never animals who were knot theorists." So the bartender tells the dog, "name a knot invariant," and it goes "Arf, arf!!" He asks the cow the same thing and it goes "Mu, Mu!!" The bartender says "very funny" and kicks them all out. Outside the dog asks his friend, "should I have said the Jones polynomial instead?" If you want to learn a little bit about knots, knot invariants, and why this joke is funny (it's kinda funny) come check out the talk.
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Nathaniel Bannister
2020-03-02
We enter the world of finite topological spaces and show a strange world of interesting spaces, including a space with six points and infinitely many nonzero homotopy groups. More generally, for each n, there is a space with 2n+2 points with the same homotopy groups as the sphere $S^n$. We will show this construction and more, detailing what we can-and cannot-do homotopically with finite spaces.
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Alex Xue
2020-03-02
Helly's theorem is a fundamental result about the intersection properties of convex sets. It states that given $n$ convex sets in $\mathbb{R}^d$, if the intersection of every $d + 1$ convex sets is non-empty, then the intersection of all the convex sets is non-empty. In 1982, B\'ar\'any, Katchalski, and Pach proved a volumetric extension of Helly's theorem stating that if the intersection of every $2d$ of the convex sets has volume at least one, then the volume of the intersection of all the sets is at least $d^{-2d^2}$. This loss factor in the volume of the intersection is necessary. With additional constraints on the intersections, we can embed the convex sets in a higher dimension to obtain exact volumetric Helly results that avoid the loss factor. Other quantitative Helly-type theorems can be obtained with the same techniques. Joint work with Sherry Sankar and Pablo Sober\'on.
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Jessie Tan
2020-02-17
Mersenne primes are primes that are one less than a power of two. They are very useful for forming even perfect numbers, but very useless for RSA encryption. Besides Euler's enhanced trial factoring and the Lucas-Lehmer test, we haven't made much progress at understanding them. Millions of CPUs are currently searching of those primes brute-force, but no one knows if we will find another.
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Undergraduate Math Club
2020-02-10
Each speaker will give short talks. Come taste a variety of different topics! AA: A fractal staircase helps us understand many physical phenomena. NJ: Symmetry is adored by mathematicians, but did you know it's loved by chemists too? DL: Math inspires String Theory, and vice versa. We will explore some of these connections. MM: We will solve a pendulum's equation of motion exactly. JT: Will we find another Mersenne prime?
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Cornell Math Department
2020-01-27
From 4-5pm in Mallot 532 there will be an information session for the SPUR and REU programs hosted by Cornell.
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Cornell Math Club
2019-12-09
The Cornell Math Club's first meeting will be a Games Session in Mallot 532 from 6-7pm. Free Pizza and Juice will be provided.
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Isaac Legred
2019-12-09
Have you ever pondered what a 3-sphere looks like embedded in full 4 dimensional glory? Or why your hair always seems to have a cowlick? Or maybe why LIGO detectors look the way they do? These and many more questions are all related to a curious bit of Geometry known as the Hopf Map (sometimes the Hopf Fibration, or Hopf Bundle). At the surface, the Hopf Map is a differentiable function from the 3-sphere (the set of all points in four dimensional space which are distance 1 from the origin), to the 2-sphere (good old, everyday, surface-of-the-Earth 2-sphere) which squashes circles to points. In it, though, we can see some strange asymmetries in geometry, some strange symmetries in our universe, and maybe even get some more fibers into our mathematical diet.
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Philip Sink
2019-12-02
We will explore the foundations and motivations of Justification Logic and its relationship to Provability Logic, noting in particular its relationship to Godels original conception for a logic of proofs. Time permitting, we will look into some original results in Topological Semantics for LP(CS) and the relationship between modality, topology, and intuitionism.
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Linus Setiabrata
2019-11-25
Suppose we are given a quadratic polynomial Q and some initial data, and we wanted to study the recurrence relation defined by Q. Unfortunately the quadratic-ness gives two possible next terms, so partial solutions to this recurrence should be indexed by a 2-branching tree; full solutions to the recurrence should be indexed by a choice of branch. All of these branches are made equally, because they are governed by the same initial data and the same Q. It turns out that sometimes, some branches are more equal than others. I hope to explain to you why this is the case. If time permits, I hope to outline some joint work with Sergey Fomin.
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Thomas Watts
2019-11-18
How hard could it possibly be to solve 4x^3-g_2x-g_3=0 for x a complex number.
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Arthur Tanjaya
2019-11-11
In 1980, Rabin modified Millers primality test to obtain a polynomial-time probabilistic primality test. This was one of the first discoveries of a non-deterministic algorithm that is asymptotically faster than its best known deterministic analog. We will discuss several modern algorithms and data structures that employ nondeterminism for speed, and explore how randomness helps them run faster. Additionally, it is currently an open problem whether Turing machines with access to randomness can run strictly faster than those without; if time permits, we will go into a brief discussion of this.
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Cornell Math Department
2019-10-28
Discover the many opportunities in math, including spring class offerings, study abroad, the major, and the minor. Meet fellow math sutents and faculty. Snacks will be served. Drop in any time before 5:00pm.
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Leo Huang
2019-10-21
Bayesian optimization is a surrogate optimization method for expensive, black-box functions. It uses Gaussian process regression to quantify the uncertainty in the surrogate and continuously updates the GP with each new function evaluation. Key components are the kernel function -- which measures similarity between data points -- and the acquisition function -- which strikes a balance between exploration and exploitation. In this talk, we take a look at the underlying machinery and give live demos using MATLAB.
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Frankie Chan
2019-10-07
When L/K is a finite Galois extension of fields, we have a beautiful inverse correspondence between the intermediate fields of L/K with the subgroups of the automorphism group Gal(L/K). We can attempt to extend this notion to infinite algebraic field extensions, but the previous correspondence fails to hold. We will see an example of why not; nevertheless, there fortunately is still a correspondence. In this talk, we will quickly revisit the finite theory and discuss the correct way to think about the infinite Galois correspondence by the way of profinite groups. It is useful to know elementary topology and basic definitions from field theory. Given enough time, details may be provided, but this talk is more to provide enough language to show the results.
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Jake Januzelli
2019-09-30
Broadly, analytic number theory is the study of the analytic aspects of the objects of number theory. Counting solutions of polynomial equations, estimating the number of prime divisors of an integer $\sim N$, and bounding the first prime in an arithmetic progression are all examples of analytic number theory. This talk will outline some of the main techniques and problems in analytic number theory, with a focus on exposition and ideas instead of proofs.
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Ely Sandine
2019-09-23
In this talk we will talk about Ordinary Differential Equations. By using the Fundamental Theorem of Calculus as the main uniqueness theorem, we will re-derive properties of trig and exponential functions including their derivatives, addition formulas, power series expansions, and Eulers identity. We will then think more about uniqueness and existence. Consider the equations dx/dt=x^2 and dx/dt=sqrt(abs(x)). The first has solutions that go to infinity in finite time and the second has multiple solutions for a given initial condition. We will think about these, along with 2d linear systems. Putting this all together, we will think about resonance, and explain why forced oscillators get so crazy.
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Caleb Koch
2019-09-11
Boolean circuits are a restricted model of computation where one can find many interesting lower bound results. One such result is that, for n large enough, the parity of n bits cannot be computed by constant-depth, polynomial-size circuits with unbounded fan-in. Ill discuss the Razborov-Smolensky proof tof this lower bound using the method of approximation after reviewing some requisite circuit complexity. Please note the unusual schedule - this talk with be on a Wednesday.
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Cornell Math Club
2019-08-29
Welcome back to school! Come to Mallot 532 this Thursday for board games, pizza, and people.
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Sumun Iyer
2019-05-06
Given a commutative ring R, we can define the unitary Cayley graph of R as the graph with vertices labeled by the elements of R, with x adjacent to y if and ony if x-y is a unit in R. These graphs are full of symmetry and structure-which often makes computing graph parameters for them quite nice. We will talk about why these graphs are important, investigate some connections to number theory, and then play around with various graph parameters. This talk should require no background to understand and will end with some fun problems to try.
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Arthur Tanjaya
2019-04-29
In 2001, we had a breakthrough: Shors algorithm was used to factor 15 in polynomial time. We will begin with a brief rundown of the mathematics involvded in quantum computation, such as qubits and entanglement, and see why linear algebra lets us have our cake and eat it too. The talk will focus on the construction of several quantum logic gates, such as the Toffoli and Hadamard gates, which we will leverage to prove that quantum circuits are actually capable of faster computation than classical ones. If time permits, we willhopefully get to an overview of Shors algorithm.
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Rebecca Jiang
2019-04-22
A falling cat tends to land on its feet, if given enough time, even for non-upright, non-rotating initial conditions. This poses an apparent paradox. The cat has access to no external torques, and therefore angular momentum is conserved and zero during the cats fall. How can the cat flip itself over?
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Steve Trettel
2019-04-17
The surface of the earth is curved, a fact one can notice intrinsically by taking a friend to the equator and both walking straight north: initially you two begin your journey walking parallel to one another, but eventually collide at the north pole. Mathematically speaking, the positive curvature of the earth causes the straight line (geodesic) paths you two are walking on to converge. While harder to visualize, curvature is an important property of 3-dimensional spaces as well, and gaining intuition about curved 3-dimensional worlds leads to some fun mathematical thought experiments!
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Math Majors Committee
2019-04-15
Please come and tell me what we are doing right, what we are doing wrong, and what else we might be doing. Oh and there will be FREE PIZZA!
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Cornell Math Department
2019-04-10
Discover the many opportunities in math, including fall class offerings, summer programs, the major, and the minor. Meet fellow math students and faculty. Snacks will be served. The reception will start at 4, and one can drop by any time before 5:00 p.m.
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Philip Sink
2019-04-08
We will begin with a cursory overview of modal logic, the meaning of soundness and completeness, and the traditional axiomatic extensions. The provability logic will be motivated by Lobs theorem, and we will explore the axiomatic extension known as GL, and discover the extent to which CL is able to encapsulate provability statements in Peano arithmetic, such that the Second Incompleteness Theorem. Time permitting, we will get into the details of Solovay’s proof of the completeness of GL with respect to Peano arithmetic. The presentation will be heavily motivated by The Unprovability of Consistency by George Boolos. Please note the unusual location.
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Jake Januzelli
2019-03-25
A fundamental idea in number theory is to, given some equation, reduce it modulo some number. This is a fertile source of information: this is how one tells that, for example every prime greater than 2 that is the sum of two squares must be 1 mod 4. The subject of this talk will be the p-adic integers, which give us a way to leverage all of this information about an equation modulo some numbers. I will go over a few definitions, some basic properties and hopefully the above picture, which depicts the metric on the 3-adic integers.
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Todd Lensman
2019-03-18
The theory of optimal control provides methods to solve dynamical optimization problems in discrete and continuous time. Somewhat surprisingly, there are similarities between continuous-time control problems and static problems that arise in the study of optimal nonlinear income taxation. I will provide an introduction to continuous-time control problems and the classic solution method, Pontryagin’s Maximum Principle, and demonstrate an application of this method to optimal taxation.
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Cornell Math Club
2019-03-14
The math club is hosting a weekly meeting. This week we will be e having a pi day themed puzzle session and as always it will have pizza.
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Cornell Math Department
2019-03-14
On Pi day the math department will be hosting a pi eating contest at 1:59, to see who can eat the most pie in 3:14. For other festivities and so on, come to mallot 532.
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Amogh Anakru
2019-03-11
Julia sets are one of the most famous and beautiful examples of fractals, arising from a simple iterative rule applied to the complex numbers. I will discuss basic properties of Julia sets from the dynamical systems perspective. To explore some topological properties of Julia sets and the connection with the famous Mandelbrot set, I will prove the ~fundamental theorem of the Mandelbrot set~. Time permitting, I will explain why the Mandelbrot set is connected and discuss a very recent and amusing result on Julia sets.
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Cornell Math Club
2019-03-07
We will be hosting our weekly meetings, this week we will have lolots of board games. As usual catering will be provided by Papa Johns.
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Nikita Borisov
2019-03-04
Calculus of Variations derives conditions for finding maxima and minima of functionals (functions of functions) by slightly varying a function (here it is the input) to see how the functional value reacts. We will derive the Euler-Lagrange equation and see it in practice, finding the curve of a soup bubble over two rings and the brachistochrone. If time allows, we will look at generalizations of the Euler-Lagrange equation in higher dimensions.
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Cornell Math Club
2019-02-28
Puzzle session in 532 with pizza at 6:00?
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Maurice Pierre
2019-02-18
We will explore the reflectional and rotational transformations of the Riemann Sphere and derive the functions in the complex plane which correspond to them.
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Linus Setiabrata
2019-02-11
Combinatorics concerns itself with counting. To count more complicated things, one might try to reduce the problem to counting a simpler thing by finding a bijection between the complicated thing and the simple thing. I want to convince you that bijections are fun, and that combinatorics is like a playground. I will talk about Catalan numbers and tell you about some go the things they count; if time allows, I want to introduce root polytopes, their triangulations, and some relations to pipe dream complexes.
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Undergraduate Math Club
2019-02-07
This thursday the math club will be hosting a game session in Mallot 532 from 6-7pm. There will be pizza!
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Robert S. Strichartz and Andy Borum
2019-02-04
Wondering what to do this summer? Interested in math? Want funding to support yourself? We will talk about the Cornell summer program for undergraduate research (SPUR) and other REU programs throughout the country. Afterwards there will be an opportunity to chat with students who attended such programs in the past, both at Cornell and elsewhere.
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Daoji Huang
2018-12-03
A formal proof is a proof in which every logical inference has been checked all the way back to the fundamental axioms of mathematics. Although there is a long way to go for formalization to be practical for working mathematicians, existing theories and technologies of formal verification are already capable of formalizing a large body of modern mathematics. In this talk, I will introduce the building blocks of formal verification, including logical foundations, proof assistants, and expressing mathematics formally in such systems. In particular, I will illustrate the relevant concepts by giving a brief overview of type theories, the Coq proof assistant, and the Flyspeck project that formally verified the 400 years old Keplers Conjecture on sphere packing. Furthermore, I will discuss common challenges in formalization endeavors.
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Professor Bob Connelly
2018-11-26
Put a bunch of circular disks in a container and squeeze the container until they jam. What does the packing look like? What can you say about the density of the packing? When the disks are the same size and the container is a flat torus, the answer is known. If the Radii in ratio 1:2:3, density = 7π/24=0.92015.. sizes are random as with granular materials, for existence, there will be a minimum number of contacts. If the graph of contacts is a triangulation, often the density of the packing is quite large. Evan Solomonides and Maria Yampolskaya will demonstrate a simulation of packings as the container contracts until they jam.
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Jack Cook
2018-11-19
Using the tools of smooth manifold theory, we propose a generalized framework for olfactory reception, learning, and processing. Inspection of the tangent bundle to a manifold yields vector fields which allow for quantification of changes. We utilize group actions to discover fibre bundles over the manifold and discover various properties related to learning. Under this paradigm, we develop a method for categorization as well as analytical tools to model changes in the category. We end with a quick discussion of searching for data on the manifold in a way that beats nearest neighbour.
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Jessie Tan
2018-11-12
The Weil Conjectures are four statements about an analogue of the Zeta function over finite fields. I’m going to talk about the roots of polynomial equations in a mod p setting, define the zeta function for a projective variety, and with the new vocabulary Ill state the Weil Conjectures at the end. Familiarity of finite fields and projective geometry is useful but not required.
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Cornell Math Club
2019-02-2-28
Puzzle session in 532 with pizza at 6:00!