AMS Student Chapter Seminar: Difference between revisions
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===September 14, Mei Rose Connor === | ===September 14, Mei Rose Connor === | ||
Title: All Things Necessary and Possible: an introduction to the Kripke semantics of modal logic | Title: All Things Necessary and Possible: an introduction to the Kripke semantics of modal logic | ||
Abstract: Modal logic is a branch of formal logic with far–reaching applications to fields such as philosophy, mathematics, computer science, and other parts of logic itself. It deals with which propositions, some of which are necessarily true (in the words of philosophy, a priori) and some of which are possibly true (analogously, a posteriori). But this will not be a philosophy talk. This talk will cover the notation, syntax, and one choice of semantics for modal logic known as the Kripke semantics. The Kripke semantics is a powerful tool that allows us to make connections between modal statements and first–order (or higher–order) logic ones. Along the way, the talk will explore how the simple symbols □ and ♢ can help to model ethics, represent the knowledge of individuals and even lead to an elegant gateway into the First Incompleteness result. | Abstract: Modal logic is a branch of formal logic with far–reaching applications to fields such as philosophy, mathematics, computer science, and other parts of logic itself. It deals with which propositions, some of which are necessarily true (in the words of philosophy, a priori) and some of which are possibly true (analogously, a posteriori). But this will not be a philosophy talk. This talk will cover the notation, syntax, and one choice of semantics for modal logic known as the Kripke semantics. The Kripke semantics is a powerful tool that allows us to make connections between modal statements and first–order (or higher–order) logic ones. Along the way, the talk will explore how the simple symbols □ and ♢ can help to model ethics, represent the knowledge of individuals and even lead to an elegant gateway into the First Incompleteness result. | ||
===September 21, Sun Woo Park === | ===September 21, Sun Woo Park === | ||
Title: What I did in my military service II (A functorial formulation of deep learning algorithms) | Title: What I did in my military service II (A functorial formulation of deep learning algorithms) | ||
Abstract: Even though deep learning algorithms (say convolutional neural networks, graph neural networks, and attention-transformers) show outstanding performances in executing certain tasks, there are also certain tasks that these algorithms do not perform well. We'll try to give a naive attempt to understand why such problems can occur. Similar to last semester, I will once again recall what I was interested in during the last few months of my 3-year military service in South Korea. | Abstract: Even though deep learning algorithms (say convolutional neural networks, graph neural networks, and attention-transformers) show outstanding performances in executing certain tasks, there are also certain tasks that these algorithms do not perform well. We'll try to give a naive attempt to understand why such problems can occur. Similar to last semester, I will once again recall what I was interested in during the last few months of my 3-year military service in South Korea. | ||
===September 28, Caroline Nunn=== | ===September 28, Caroline Nunn=== | ||
Title: Phinary Numbers | Title: Phinary Numbers | ||
Abstract: Everyone and their grandmother knows about binary numbers. But do you know about phinary numbers? In this talk, we will explore the fun consequences of using an irrational number base system. We will define phinary representations of real numbers and explore which real numbers can be written using finite or recurring phinary representations. | Abstract: Everyone and their grandmother knows about binary numbers. But do you know about phinary numbers? In this talk, we will explore the fun consequences of using an irrational number base system. We will define phinary representations of real numbers and explore which real numbers can be written using finite or recurring phinary representations. | ||
===October 5, Gabriella Brown=== | ===October 5, Gabriella Brown=== | ||
Title: Topological Entropy in Shift Spaces | Title: Topological Entropy in Shift Spaces | ||
Abstract: Entropy is a concept that many STEM disciplines engage with, which results in many different perspectives on what exactly it is. This talk will introduce the perspective of symbolic dynamics by defining shifts of finite type and showing how to compute their topological entropy. | Abstract: Entropy is a concept that many STEM disciplines engage with, which results in many different perspectives on what exactly it is. This talk will introduce the perspective of symbolic dynamics by defining shifts of finite type and showing how to compute their topological entropy. | ||
===October 12, Nakid Cordero=== | ===October 12, Nakid Cordero=== | ||
Title: How to prove the Riemann Hypothesis: a logician's approach | Title: How to prove the Riemann Hypothesis: a logician's approach | ||
Abstract: ''Hint:'' ''Prove that you cannot disprove it.'' | Abstract: ''Hint:'' ''Prove that you cannot disprove it.'' | ||
===October 19, Ari Davidovsky=== | ===October 19, Ari Davidovsky=== | ||
Title: Using Ultrafilters in Additive Combinatorics | Title: Using Ultrafilters in Additive Combinatorics | ||
Abstract: The goal of this talk is to introduce the idea of ultrafilters and show how they help us prove some cool results from additive combinatorics. The main result proved will be Hindman's Theorem which states if we partition the natural numbers into finitely many sets then one of these sets A contains an infinite subset B such that the sum of any finitely many distinct elements in B will always be in A. | Abstract: The goal of this talk is to introduce the idea of ultrafilters and show how they help us prove some cool results from additive combinatorics. The main result proved will be Hindman's Theorem which states if we partition the natural numbers into finitely many sets then one of these sets A contains an infinite subset B such that the sum of any finitely many distinct elements in B will always be in A. | ||
===October 26, Otto Baier=== | ===October 26, Otto Baier=== | ||
Title: "Circulant Matrices and the Discrete Fourier Transform" | Title: "Circulant Matrices and the Discrete Fourier Transform" | ||
Abstract: "Have you ever tried to use a finite difference method on a differential equation with periodic boundary conditions and said, 'I wonder how I could find the eigenvalues of this matrix analytically'? No? Well either way, you're going to find out! | Abstract: "Have you ever tried to use a finite difference method on a differential equation with periodic boundary conditions and said, 'I wonder how I could find the eigenvalues of this matrix analytically'? No? Well either way, you're going to find out! | ||
===November 2, Speaker TBA=== | ===November 2, Speaker TBA=== | ||
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===November 9, Owen Goff=== | ===November 9, Owen Goff=== | ||
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===November 16, Speaker TBA=== | ===November 16, Speaker TBA=== | ||
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===November 30, Speaker TBA=== | ===November 30, Speaker TBA=== | ||
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===December 7, Speaker TBA=== | ===December 7, Speaker TBA=== | ||
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===December 14, Maybe Cancelled?=== | ===December 14, Maybe Cancelled?=== | ||
Revision as of 22:24, 25 October 2023
The AMS Student Chapter Seminar (aka Donut Seminar) is an informal, graduate student seminar on a wide range of mathematical topics. The goal of the seminar is to promote community building and give graduate students an opportunity to communicate fun, accessible math to their peers in a stress-free (but not sugar-free) environment. Pastries (usually donuts) will be provided.
- When: Wednesdays, 3:30 PM – 4:00 PM
- Where: Van Vleck, 9th floor lounge (unless otherwise announced)
- Organizers: Ivan Aidun, Kaiyi Huang, Ethan Schondorf
Everyone is welcome to give a talk. To sign up, please contact one of the organizers with a title and abstract. Talks are 25 minutes long and should avoid assuming significant mathematical background beyond first-year graduate courses.
The schedule of talks from past semesters can be found here.
Fall 2023
September 7, Alex Mine
Title: My Favorite Fact about Continued Fractions
September 14, Mei Rose Connor
Title: All Things Necessary and Possible: an introduction to the Kripke semantics of modal logic
Abstract: Modal logic is a branch of formal logic with far–reaching applications to fields such as philosophy, mathematics, computer science, and other parts of logic itself. It deals with which propositions, some of which are necessarily true (in the words of philosophy, a priori) and some of which are possibly true (analogously, a posteriori). But this will not be a philosophy talk. This talk will cover the notation, syntax, and one choice of semantics for modal logic known as the Kripke semantics. The Kripke semantics is a powerful tool that allows us to make connections between modal statements and first–order (or higher–order) logic ones. Along the way, the talk will explore how the simple symbols □ and ♢ can help to model ethics, represent the knowledge of individuals and even lead to an elegant gateway into the First Incompleteness result.
September 21, Sun Woo Park
Title: What I did in my military service II (A functorial formulation of deep learning algorithms)
Abstract: Even though deep learning algorithms (say convolutional neural networks, graph neural networks, and attention-transformers) show outstanding performances in executing certain tasks, there are also certain tasks that these algorithms do not perform well. We'll try to give a naive attempt to understand why such problems can occur. Similar to last semester, I will once again recall what I was interested in during the last few months of my 3-year military service in South Korea.
September 28, Caroline Nunn
Title: Phinary Numbers
Abstract: Everyone and their grandmother knows about binary numbers. But do you know about phinary numbers? In this talk, we will explore the fun consequences of using an irrational number base system. We will define phinary representations of real numbers and explore which real numbers can be written using finite or recurring phinary representations.
October 5, Gabriella Brown
Title: Topological Entropy in Shift Spaces
Abstract: Entropy is a concept that many STEM disciplines engage with, which results in many different perspectives on what exactly it is. This talk will introduce the perspective of symbolic dynamics by defining shifts of finite type and showing how to compute their topological entropy.
October 12, Nakid Cordero
Title: How to prove the Riemann Hypothesis: a logician's approach
Abstract: Hint: Prove that you cannot disprove it.
October 19, Ari Davidovsky
Title: Using Ultrafilters in Additive Combinatorics
Abstract: The goal of this talk is to introduce the idea of ultrafilters and show how they help us prove some cool results from additive combinatorics. The main result proved will be Hindman's Theorem which states if we partition the natural numbers into finitely many sets then one of these sets A contains an infinite subset B such that the sum of any finitely many distinct elements in B will always be in A.
October 26, Otto Baier
Title: "Circulant Matrices and the Discrete Fourier Transform"
Abstract: "Have you ever tried to use a finite difference method on a differential equation with periodic boundary conditions and said, 'I wonder how I could find the eigenvalues of this matrix analytically'? No? Well either way, you're going to find out!
November 2, Speaker TBA
Title:
Abstract:
November 9, Owen Goff
Title:
Abstract:
November 16, Speaker TBA
Title:
Abstract:
November 23, CANCELLED FOR THANKSGIVING
November 30, Speaker TBA
Title:
Abstract:
December 7, Speaker TBA
Title:
Abstract: