Logic Seminar Pi Math Cornell Edu

Consult the weekly seminar bulletin for a list of talks for the seminars listed below and other mathematical seminars on campus. Seminars in related fields:CAM Colloquium, CS Theory Seminar, ORIE Colloquium, Statistics Seminar This is a survey talk about idealistic equivalence relations. I will discuss open questions and revise a result by Becker showing that under analytic determinacy there is an idealistic equivalence relation that does not arise from any Borel action of Polish groups in... The talk contains joint work (in preparation) with Luca Motto Ros. The Borel chromatic number of an analytic graph is the definable counterpart of its chromatic number: instead of considering general colorings of pairs, we look at colorings with Borel sections only.

It turns out - from the work from Kechris, Solecki and Todorcevic - that there exists a least possible Borel chromatic number among all analytic graphs: the one of $G_0$. In this talk, we will see how to separate uncountable Borel chromatic numbers between themselves, and from other cardinal characteristics of the continuum. We will also address some ongoing work on the graph generated by the Turing reducibility relation, and metric graphs defined for families of countable distances converging to zero. Course information provided by the 2025-2026 Catalog. A twice weekly seminar in logic. Typically, a topic is selected for each semester, and at least half of the meetings of the course are devoted to this topic with presentations primarily by students.

Opportunities are also provided for students and others to present their own work and other topics of interest. Last 4 Terms Offered 2025SP, 2024SP, 2022SP, 2021SP 3 Credits Sat/Unsat(Satisfactory/Unsatisfactory) To be determined. There are currently no textbooks/materials listed, or no textbooks/materials required, for this section. Additional information may be found on the syllabus provided by your professor.

The number π (/paɪ/ ⓘ; spelled out as pi) is a mathematical constant, approximately equal to 3.14159, that is the ratio of a circle's circumference to its diameter. It appears in many formulae across mathematics and physics, and some of these formulae are commonly used for defining π, to avoid relying on the definition of the length of a curve. The number π is an irrational number, meaning that it cannot be expressed exactly as a ratio of two integers, although fractions such as 22 7 {\displaystyle {\tfrac {22}{7}}} are commonly used to approximate... Consequently, its decimal representation never ends, nor enters a permanently repeating pattern. It is a transcendental number, meaning that it cannot be a solution of an algebraic equation involving only finite sums, products, powers, and integers. The transcendence of π implies that it is impossible to solve the ancient challenge of squaring the circle with a compass and straightedge.

The decimal digits of π appear to be randomly distributed, but no proof of this conjecture has been found. For thousands of years, mathematicians have attempted to extend their understanding of π, sometimes by computing its value to a high degree of accuracy. Ancient civilizations, including the Egyptians and Babylonians, required fairly accurate approximations of π for practical computations. Around 250 BC, the Greek mathematician Archimedes created an algorithm to approximate π with arbitrary accuracy. In the 5th century AD, Chinese mathematicians approximated π to seven digits, while Indian mathematicians made a five-digit approximation, both using geometrical techniques. The first computational formula for π, based on infinite series, was discovered a millennium later.

The earliest known use of the Greek letter π to represent the ratio of a circle's circumference to its diameter was by the Welsh mathematician William Jones in 1706. The invention of calculus soon led to the calculation of hundreds of digits of π, enough for all practical scientific computations. Nevertheless, in the 20th and 21st centuries, mathematicians and computer scientists have pursued new approaches that, when combined with increasing computational power, extended the decimal representation of π to many trillions of digits. These computations are motivated by the development of efficient algorithms to calculate numeric series, as well as the human quest to break records. The extensive computations involved have also been used to test the correctness of new computer processors. Because it relates to a circle, π is found in many formulae in trigonometry and geometry, especially those concerning circles, ellipses and spheres.

It is also found in formulae from other topics in science, such as cosmology, fractals, thermodynamics, mechanics, and electromagnetism. It also appears in areas having little to do with geometry, such as number theory and statistics, and in modern mathematical analysis can be defined without any reference to geometry. The ubiquity of π makes it one of the most widely known mathematical constants inside and outside of science. Several books devoted to π have been published, and record-setting calculations of the digits of π often result in news headlines. The symbol used by mathematicians to represent the ratio of a circle's circumference to its diameter is the lowercase Greek letter π, sometimes spelled out as pi.[1] In English, π is pronounced as "pie"...

People Also Search

• Logic Seminar | pi.math.cornell.edu
• Colloquia and Seminars | pi.math.cornell.edu
• Seminar Bulletin - pi.math.cornell.edu
• pi.math.cornell.edu | Department of Mathematics
• Class Roster - Spring 2026 - MATH 7820 - classes.cornell.edu
• Pi - Wikipedia