The Mathematics Department of the University of Minnesota welcomes you to the Junior Colloquium! When school is in session, the Junior Colloquium is held every Monday at 12:20 P.M. in Vincent Hall 16. There will be cookies! Talks are intended to be accessible and interesting to a broad audience, from undergraduate math students to faculty.
The current organizers of the Junior Colloquium are Prof. Richard McGehee, Alexander Garver, and Becky Patrias. If you have questions about the seminar, or would like to recommend a speaker, please contact an organizer. Graduate students are especially encouraged to volunteer!
For questions about the web page please contact Becky Patrias.
| Date | Speaker | Topic |
| January 23 | Trevor Bain |
Myhill and Nerode: relations given by distinguishing extensions and their fellow automatons |
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I'll cover the basics of Formal Languages. Then we'll examine a few languages to get a feel for the subject. Finally, I'll present the Myhill-Nerode theorem which gives necessary and sufficient conditions for a formal language being "regular".
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| January 30 | Erin Manlove |
Topology of Robot Arms |
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We examine planar robot arms, which consist of fixed lengths connected by revolving joints. We will use ideas from topology and geometry to describe the region that a robot arm can reach.
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| February 6 | John Goes |
A Gentle Introduction to the P-adics |
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We will define the p-adic numbers and discuss the topology induced by the p-adic metric. Using basic p-adic analysis, we will prove a couple of elementary results. Finally we will briefly discuss the role of the p-adics in number theory, particularly local-global results.
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| February 13 | John Lee |
Elastic and Viscoelastic Materials |
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Elastic and viscoelastic properties of materials are important to understand kinematics of materials in continuum mechanics. I will introduce basic concepts of continuum mechanics in a rather intuitive approach and discuss some properties of linear elastic and viscoelastic materials.
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| February 20 | Jonathan Hill |
Death of a Salesman: Demonstrating that the Traveling Salesman Problem is NP-Hard |
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Like the Four Color Theorem and Fermat's Last Theorem before it, the proposition that the Traveling Salesman Problem (TSP) cannot be quickly solved seems a foregone conclusion. Yet it remains unproven. We will familiarize ourselves with the concepts of complexity theory, and using these techniques demonstrate that the TSP is at least as difficult as a handful of other difficult problems. In the terms of that theory, we will show that the TSP is NP-Hard.
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| February 27 | Professor Jonathan Rogness |
Unraveling the Strangest Definition in Math 8301 |
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Homotopic maps and chain complexes are fundamental topics in algebraic topology, but the definition of "chain homotopic maps" strikes most students as strange. The ladder-like diagram in the definition includes an odd map which points diagonally across the squares in the commutative diagram. Why does the definition require these maps between different dimensions of the two chain complexes? We'll answer the question by taking a "folk viewpoint" in which chain complexes are treated like CW-complexes, making the definition of chain homotopies exactly match up with the familiar geometric definition.
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| March 5 | Julie Leifeld |
Budyko's Energy Balance Climate Model |
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In a 1968 paper, Budyko introduced the idea that the
temperature of the earth can be modeled using a simple energy balance
model. I will explain the ideas behind this classic model, and
discuss some modifications which must be made to make sense of the
dynamics of the system.
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| March 19 | Jonas Karlsson |
A not non-interesting talk on intuitionistic logic |
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What is intuitionistic logic? Why did it make Hilbert furious? How is a quantum computer different from a classical one? What would the world be like if it were not made by sets? Will Jonas actually answer any of these questions or will he just keep asking new ones? Come and see for yourself.
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| March 26 | Nathan Williams |
Beatty Sequences |
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We will discuss Beatty Sequences, Rayleigh's theorem, and generalizations.
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| April 2 | Vishal Saraswat |
Searchable Encryption |
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Public-key encryption schemes with keyword search (PEKS) allows a sender to compute an encrypted message, so that the receiver can allow a third party to search keywords in the encrypted message without additional loss of privacy on the content of the message.
Suppose user Alice wishes to read her email on a number of devices: laptop, desktop, pager, etc. Alice's mail gateway is supposed to route email to the appropriate device based on the keywords in the email. For example, when Bob sends email with the keyword "urgent" the mail is routed to Alice's pager. When Bob sends email with the keyword "lunch" the mail is routed to Alice's desktop for reading later.
Now, suppose Bob sends encrypted email to Alice using Alice's public key. Both the contents of the email and the keywords are encrypted. In this case the mail gateway cannot see the keywords and hence cannot make routing decisions.
With PEKS one can enable Alice to give the gateway the ability to test whether "urgent" is a keyword in the email, but the gateway learns nothing else about the email. More generally, Alice can specify a few keywords that the mail gateway can search for, but learn nothing else about incoming mail.
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| April 9 | Robbie Hank |
Computational Algebraic Topology |
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The study of topology has something to do with looking at the shapes of things. A coffee cup and donut are the same thing topologically (and I'm told taste pretty good together too), while the letters A and B are different topologically because they have a different number of loops. But why is this useful?
Computational algebraic topology is an exciting new field that allows us to analyze data using structures and techniques from algebraic topology. Persistent homology is a way to take a small collection of data points and analyze its structure without knowing the complete picture. Insights from putting structure on the data can be useful, for example, in character recognition or optimizing systems according to an analysis. In this talk, we will review necessary definitions from algebraic topology and provide an overview of the constructions related to this field.
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| April 16 |
No Junior Colloquium today due to written prelims |
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| April 23 | Richard McGehee |
Why the school of mathematics appreciates our graduate students |
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A few words from Professor McGehee followed by open discussion.
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| April 30 | Thomas McConville |
Combinatorial Hodge Theory or: How to avoid doing analysis |
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Hodge's theorem gives an isomorphism between harmonic forms and cohomology. We will view this statement combinatorially on simplicial complexes. This will provide an excuse to talk about graph laplacians, matrix-tree theorem, random walks, chessboard complexes, representations of symmetric groups, etc.
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The Junior Colloquium evolved from the ATaC seminar -- an acronym for "All Topics Are Considered," previously "Algebra, Topology and Combinatorics." [The name is due to Dr. Peter Webb.]