srtop
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| - | < | + | ====== |
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| - | < | + | ===== Logistics |
| - | <p>For Spring 2026, this seminar meets weekly on Mondays from 4-5:00pm in MSB 1147. The seminar is co-organized by Trevor Oliveira-Smith and Alex Simons. If you have any questions you can reach out via email at tdoliveirasmith@ucdavis.edu and asimons@ucdavis.edu | + | |
| + | For Spring 2026, this seminar meets weekly on Mondays from 4-5:00pm in MSB 1147. The seminar is co-organized by Trevor Oliveira-Smith and Alex Simons. If you have any questions you can reach out via email at <tdoliveirasmith@ucdavis.edu> and <asimons@ucdavis.edu> | ||
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| + | For the purposes of advertising the talks each week and sending out general information about topology/geometry at Davis, we will use the following listserv: < | ||
| + | |||
| + | ===== Description ===== | ||
| - | <p> For the purposes of advertising the talks each week and sending out general information about topology/ | ||
| - | You can email asimons@ucdavis.edu if you would like to be added to this listserv, or you can go to lists.ucdavis.edu and search " | ||
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| The purpose is to encourage students studying geometry/ | The purpose is to encourage students studying geometry/ | ||
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| - | Talks will conceivably cover a broad spectrum, but in general, we envision not-too-technical talks emphasizing ideas. | ||
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| - | If you would like to give a talk, please email the seminar organizers (see Logistics above). The tentative schedule is available here:</ | ||
| - | < | + | Talks will conceivably cover a broad spectrum, but in general, we envision not-too-technical talks emphasizing ideas. Talks are by students for students, but everyone is welcome. We also encourage speakers to take 2-3 seminars to delve into a topic in depth. Practice qualifying exam talks are typically given in the [[http:// |
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| - | < | + | ===== Schedule Information ===== |
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| - | < | + | If you would like to give a talk, please email the seminar organizers (see Logistics above). The tentative schedule is available here: |
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| - | < | + | ==== Spring 2026 ==== |
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| - | < | + | * Apr 6: Trevor Oliveira-Smith: " |
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| + | ===== Possible Seminar Topics ===== | ||
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| + | Anybody is welcome to talk about mathematics related to topology. If you would like to talk about something but don't have a topic, here are some suggestions. | ||
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| + | The list below may be helpful in your search for a topic. Some items are specific talk ideas while others are keywords to look up and investigate, | ||
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| + | For the more intrepid, you can find topics by looking through the [[http:// | ||
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| + | In addition, you can ask more experienced students and learn what they find interesting. The organizers are also happy to lend a hand in preparing a talk. | ||
| + | |||
| + | ==== Beginner ==== | ||
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| + | * Map colorings and the five color theorem | ||
| + | * Different proofs of Euler' | ||
| + | * Gauss-Bonnet formula - concept, applications, | ||
| + | * Brouwer fixed point theorem -- different proofs, e.g. using Hex or Sperner' | ||
| + | * Conway' | ||
| + | * Dehn's solution to Hilbert' | ||
| + | * Take some family of knots and explain some interesting problems (solved and unsolved) about them. For example, alternating knots, 2-bridge knots, arborescent knots, Montesinos knots. | ||
| + | * Basic properties of knot genus and some results and conjectures | ||
| + | * The lens spaces L(5,1) and L(5,2) are not homeomorphic (a la Alexander) | ||
| + | * Wild/ | ||
| + | * Horned spheres and crumbled cubes | ||
| + | * Wild arcs -- Fox-Artin arcs | ||
| + | * The Hopf Fibration | ||
| + | * Whitehead manifold | ||
| + | * Lamplighter groups | ||
| + | * Heegaard splittings | ||
| + | * Legendrian knots (definition and classical invariants) | ||
| + | * Find an unsolved problem in Adams' //The Knot Book// and explain work that's been done on it | ||
| + | |||
| + | ==== Intermediate ==== | ||
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| + | * Trisections | ||
| + | * Symplectic and/or contact manifolds | ||
| + | * " | ||
| + | * e.g. in Gauss-Gersten-Stallings proof of the fundamental thm of algebra | ||
| + | * Four color theorem | ||
| + | * Explain main ideas of proof, e.g. " | ||
| + | * Relation to Lie algebras | ||
| + | * Yang-Baxter equation | ||
| + | * Use Conway notation to classify Euclidean 2-orbifolds/ | ||
| + | * Circle packings and Andreev' | ||
| + | * Lickorish Twist theorem | ||
| + | * Isometric embeddings of the hyperbolic plane into R^3 | ||
| + | * Topological proofs of Kneser' | ||
| + | * Rubinstein-Thompson 3-sphere recognition algorithm | ||
| + | * Essential surfaces in knot complements take only finitely many boundary slopes | ||
| + | * Classification of Lens Spaces | ||
| + | * An Overview of the Eight 3-dimensional Geometries | ||
| + | * Interesting unknot diagrams and the unknotting problem | ||
| + | * Brown' | ||
| + | * Finite type invariants of knots and 3-manifolds | ||
| + | * Dehn's problems and word-hyperbolic groups | ||
| + | * Recognizing hyperbolic 3-manifolds via SnapPea | ||
| + | * The curve complex and distances of Heegaard splittings | ||
| + | * Pick a topic from Lickorish' | ||
| + | * Survey of results on knotted | ||
| + | * //A sample of results//: | ||
| + | * No smooth circle knots in R^4 - it would be interesting to just explain the //real// proof of this | ||
| + | * Zeeman - PL knotting cannot occur in codimension | ||
| + | * The question of whether PL knotting occurs in codimension 1 is called the PL Schoenflies problem | ||
| + | * Haefliger - smooth knotting can occur in codimensions > 2, e.g. smoothly knotted S^3 in S^6 | ||
| + | * Stallings - two S^50's link in dimensions 101, 100, 99, 98, but unlink in 97, 96, and then link again in 95, 94, ..., ??? , ..., 52. | ||
| + | * 4-dimensional Schoenflies problem | ||
| + | * Quantum algorithms and the Jones polynomial | ||
| + | * Equivariant versions of loop and sphere theorems | ||
| + | |||
| + | ==== Advanced ==== | ||
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| + | * Choose an unsolved problem on the Kirby problem list and explain the most recent progress on that problem. | ||
| + | * Double suspension of the Mazur homology 3-sphere is the 5-sphere | ||
| + | * //Suggested reference//: | ||
| + | * Milnor' | ||
| + | * //Suggested reference//: | ||
| + | * Thurston' | ||
| + | * Smales' | ||
| + | * Perelman' | ||
| + | * //Suggested reference//: | ||
| + | * Heegaard Floer homology | ||
| + | * Casson invariant | ||
| + | * Volume Conjectures | ||
| + | * Is Weeks manifold the smallest closed hyperbolic 3-manifold? | ||
| + | * Jones polynomial and volume | ||
| + | * Khovanov Homology and volume | ||
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| + | ===== Previous Talks ===== | ||
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| + | ==== Winter 2026 ==== | ||
| + | * Jan 5: Trevor Oliveira-Smith: | ||
| + | * Jan 12: Trevor Oliveira-Smith: | ||
| + | * Jan 19: MLK Day (no seminar) | ||
| + | * Jan 26: Zach Ibarra: " | ||
| + | * Feb 2: | ||
| + | * Feb 9: Alex Simons " | ||
| + | * Feb 16: President' | ||
| + | * Feb 23: Cindy Zhang: "The h-cobordism theorem" | ||
| + | * Mar 2: Ian Sullivan " | ||
| + | * Mar 9: CANCELLED due to sick speaker | ||
| - | < | + | ==== Fall 2025 ==== |
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| - | Anybody is welcome to talk about mathematics related to topology. | + | |
| - | <p> | + | |
| - | The list below may be helpful in your search for a topic. | + | |
| - | <p> | + | |
| - | For the more intrepid, you can find topics by looking through the <a href=" | + | |
| - | </ | + | |
| - | <p> | + | |
| - | In addition, you can ask more experienced students and learn what they find interesting. | + | |
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| - | <li> Heegaard splittings</ | + | |
| - | <li> Legendrian knots (definition and classical invariants) </ | + | |
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| - | <li> Trisections </ | + | |
| - | <li> Symplectic and/or contact manifolds</ | + | |
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| - | <li> Choose an unsolved problem on the Kirby problem list and explain the most recent progress on that problem.</ | + | |
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| - | Wiley, New York (expository article)</ | + | |
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| - | < | + | * Sep 29: Alex Simons: "A hyperbolic structure on the figure eight knot complement" |
| + | * Oct 6: Trevor Oliveira-Smith: | ||
| + | * Oct 13: Cancelled for Indigenous People' | ||
| + | * Oct 20: Cancelled (scheduled speaker was sick) | ||
| + | * Oct 27: Trevor Oliveira-Smith: | ||
| + | * Nov 3: Bryce Thomson: " | ||
| + | * Nov 10: Cancelled (scheduled speaker was sick) | ||
| + | * Nov 17: Cindy Zhang: " | ||
| + | * Nov 24: Ian Sullivan | ||
| + | * Dec 1: Zach Ibarra: " | ||
| - | < | + | ==== Spring 2025 ==== |
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| - | <p> Mar 9: CANCELLED due to sick speaker</ | + | |
| + | * Apr 7: Bryce Thompson: " | ||
| + | * Apr 14: Josh Turner | ||
| + | * Apr 21: Evan Ortiz | ||
| + | * Apr 28: Evan Ortiz | ||
| + | * May 5: Ian Sullivan | ||
| + | * May 12: | ||
| + | * May 19: NO SEMINAR (too many folks at Georgia Topology Conference) | ||
| + | * May 26: NO SEMINAR (Memorial Day) | ||
| + | * June 2: Liza Jacoby | ||
| - | < | + | ==== Winter |
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| - | < | + | * Jan 8: Tonie Scroggin: "Understanding geometric objects through a combinatorial lens, part 1" |
| - | < | + | * Jan 22: |
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| - | < | + | * Feb 5: Ian Sullivan: " |
| - | < | + | * Feb 12: Ian Sullivan: " |
| - | < | + | * Feb 19: |
| - | < | + | * Mar 12: Zach Ibarra |
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| - | < | + | ==== Fall 2024 ==== |
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| - | < | + | * Sept 27: Trevor Oliveira-Smith "Knots in 3-manifolds" |
| - | <p>Sept 27: Trevor Oliveira-Smith "Knots in 3-manifolds" | + | |
| - | <p>Oct 2: Trevor Oliveira-Smith " | + | |
| - | <p>Oct 9: Bryce Thompson " | + | |
| - | <p>Oct 23: Daniela Cortes Rodriguez " | + | |
| - | <p>Oct 30: Zach Ibarra " | + | |
| - | <p>Nov 6: Zach Ibarra " | + | |
| - | <p>Nov 13: Alex Simons " | + | |
| - | <p>Nov 20: Alex Simons " | + | |
| - | <p>Dec 4: Annette Belleman " | + | |
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srtop.1776186464.txt.gz · Last modified: by asimons
