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| <p><h2><a name="Logistics"></a>Logistics</h2></p> | <p><h2><a name="Logistics"></a>Logistics</h2></p> | ||
| - | <p>For Winter 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 <br /><br /></p> | + | <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 <br /><br /></p> |
| <p> 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: geotopgrads@ucdavis.edu. | <p> 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: geotopgrads@ucdavis.edu. | ||
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| </p> | </p> | ||
| <p> | <p> | ||
| - | 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. | + | 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 |
| - | </p> | + | <a href="http://galois.math.ucdavis.edu/AboutDept/StudentRunSeminar"; style="text-decoration:underline;">Student Run Research Seminar</a>. |
| - | <p> | + | However, the Student Run GT Seminar is a great place for practice conference talks or if you are invited to speak at another institution's seminar. |
| - | If you would like to give a talk, but on a very introductory level, you may want to consider the <a href="http://galois.math.ucdavis.edu/AboutDept/StudentRunSeminar">pure/applied grad seminar</a>. That seminar has a general audience, while the audience for this seminar can be assumed to have familiarity with some algebraic topology and manifold theory. Practice qualifying exam talks are typically given in the <a href="http://galois.math.ucdavis.edu/AboutDept/StudentRunSeminar">pure/applied grad seminar</a>. However, this is a great place for practice conference talks or if you are invited to speak at another institution's seminar. | + | |
| </p></p> | </p></p> | ||
| <p><h2><a name="schedule"></a>Schedule Information</h2></p> | <p><h2><a name="schedule"></a>Schedule Information</h2></p> | ||
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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:</p> | If you would like to give a talk, please email the seminar organizers (see Logistics above). The tentative schedule is available here:</p> | ||
| - | <p><h3>Winter 2026</h3> | + | <p><h3>Spring 2026</h3> |
| - | <p>Jan 5: Trevor Oliveira-Smith: "Extending Singular Fibrations of 3-manifolds"</p> | + | <p> Apr 6: Trevor Oliveira-Smith: "Leveraging Kirby Diagrams"<p> |
| - | <p>Jan 12: Trevor Oliveira-Smith: "Intro to Sutured Manifolds" </p> | + | <p> Apr 13: Stephen Hutchins: "Summarizing a Proof About Diffeomorphisms of the 2-Sphere"<p> |
| - | <p>Jan 19: MLK Day (no seminar)</p> | + | <p> Apr 20: Evan Ortiz: "Curvature on Principal Bundles and Characteristic Classes"<p> |
| - | <p>Jan 26: Zach Ibarra: "Characterizations of Connections over the Field of Algebraic Numbers" </p> | + | <p> Apr 27: Can Gormez: "Contact Projective Structures "<p> |
| - | <p>Feb 2: Trevor Oliveira-Smith: "Dehn Surgery and RBG-links" </p> | + | <p> May 4: Annette Belleman<p> |
| - | <p>Feb 9: Cindy Zhang: "The h-cobordism theorem"</p> | + | <p> May 11: Cindy Zhang<p> |
| - | <p>Feb 16: President's Day (no seminar)</p> | + | <p> May 18: Daniela Cortes Rodriguez<p> |
| - | <p>Feb 23: </p> | + | <p> May 25: NO SEMINAR--HOLIDAY <p> |
| - | <p>Mar 2: </p> | + | <p> Jun 1: Soyeon Kim <p> |
| - | <p> Mar 9: </p> | + | |
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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.</p> | 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.</p> | ||
| <p> | <p> | ||
| - | 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, e.g. using <a href="http://www.ams.org/mathscinet/search/">MathSciNet</a>. There are varying levels of expected difficulty, although each topic can really be taken in deep directions. Please email the organizers with any suggestions for this list.</p> | + | 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, e.g. using <a href="http://www.ams.org/mathscinet/search/"; style="text-decoration:underline;">MathSciNet</a>. There are varying levels of expected difficulty, although each topic can really be taken in deep directions. Please email the organizers with any suggestions for this list.</p> |
| <p> | <p> | ||
| - | For the more intrepid, you can find topics by looking through the <a href="http://front.math.ucdavis.edu">arXiv</a> using categories. Relevant categories include: <a href="http://front.math.ucdavis.edu/math.GT">Geometric Topology</a> | <a href="http://front.math.ucdavis.edu/math.AT">Algebraic Topology</a> | <a href="http://front.math.ucdavis.edu/math.DG">Differential Geometry</a> | <a href="http://front.math.ucdavis.edu/math.GR">Group Theory</a>. These categories will show you the most recent submissions so you can see what people are working on. | + | For the more intrepid, you can find topics by looking through the <a href="http://front.math.ucdavis.edu"; style="text-decoration:underline;">arXiv</a> using categories. Relevant categories include: <a href="http://front.math.ucdavis.edu/math.GT"; style="text-decoration:underline;">Geometric Topology</a> | <a href="http://front.math.ucdavis.edu/math.AT"; style="text-decoration:underline;">Algebraic Topology</a> | <a href="http://front.math.ucdavis.edu/math.DG"; style="text-decoration:underline;">Differential Geometry</a> | <a href="http://front.math.ucdavis.edu/math.GR"; style="text-decoration:underline;">Group Theory</a>. These categories will show you the most recent submissions so you can see what people are working on. |
| </p> | </p> | ||
| <p> | <p> | ||
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| </p></p> | </p></p> | ||
| <p><h3>Beginner</h3> | <p><h3>Beginner</h3> | ||
| - | [Note that some of these topics may be suitable for the <a href="http://galois.math.ucdavis.edu/AboutDept/StudentRunSeminar">pure/applied grad seminar</a>. Also, one idea is to give a "basic" talk for the pure/applied grad seminar and a more advanced talk for the Student Topology Seminar.]<a class="new" href="http://galois.math.ucdavis.edu/AboutDept/StudentTopSeminar/createform?page=Note%20that%20some%20of%20these%20topics%20may%20be%20suitable%20for%20the%20%3Ca%20href%3D%22http%3A//galois.math.ucdavis.edu/AboutDept/StudentRunSeminar%22%3Epure/applied%20grad%20seminar%3C/a%3E.%20%20Also%2C%20one%20idea%20is%20to%20give%20a%20%22basic%22%20talk%20for%20the%20pure/applied%20grad%20seminar%20and%20a%20more%20advanced%20talk%20for%20the%20Student%20Topology%20Seminar." title="create this page">?</a> | + | |
| <ul> | <ul> | ||
| - | <li>Map colorings and the five color theorem</li> | + | <li style="color: #333333; background: #FFFFFF;">Map colorings and the five color theorem</li> |
| - | <li>Different proofs of Euler's formula: V - E + F =2</li> | + | <li style="color: #333333; background: #FFFFFF;">Different proofs of Euler's formula: V - E + F =2</li> |
| - | <li>Gauss-Bonnet formula - concept, applications, generalizations, etc.</li> | + | <li style="color: #333333; background: #FFFFFF;">Gauss-Bonnet formula - concept, applications, generalizations, etc.</li> |
| - | <li>Brouwer fixed point theorem -- different proofs, e.g. using Hex or Sperner's Lemma, differential topology (Sard's thm or Stoke's thm) </li> | + | <li style="color: #333333; background: #FFFFFF;">Brouwer fixed point theorem -- different proofs, e.g. using Hex or Sperner's Lemma, differential topology (Sard's thm or Stoke's thm) </li> |
| - | <li>Conway's ZIP proof of the classification of compact surfaces</li> | + | <li style="color: #333333; background: #FFFFFF;">Conway's ZIP proof of the classification of compact surfaces</li> |
| - | <li>Dehn's solution to Hilbert's 3rd problem</li> | + | <li style="color: #333333; background: #FFFFFF;">Dehn's solution to Hilbert's 3rd problem</li> |
| - | <li>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. | + | <li style="color: #333333; background: #FFFFFF;">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. |
| - | <li>Basic properties of knot genus and some results and conjectures</li> | + | <li style="color: #333333; background: #FFFFFF;">Basic properties of knot genus and some results and conjectures</li> |
| - | <li>The lens spaces L(5,1) and L(5,2) are not homeomorphic (a la Alexander)</li> | + | <li style="color: #333333; background: #FFFFFF;">The lens spaces L(5,1) and L(5,2) are not homeomorphic (a la Alexander)</li> |
| - | <li>Wild/pathological objects</li> | + | <li style="color: #333333; background: #FFFFFF;">Wild/pathological objects</li> |
| <ul> | <ul> | ||
| <li>Horned spheres and crumbled cubes</li> | <li>Horned spheres and crumbled cubes</li> | ||
| <li>Wild arcs -- Fox-Artin arcs</li> | <li>Wild arcs -- Fox-Artin arcs</li> | ||
| </ul> | </ul> | ||
| - | <li>The Hopf Fibration</li> | + | <li style="color: #333333; background: #FFFFFF;">The Hopf Fibration</li> |
| - | <li>Whitehead manifold</li> | + | <li style="color: #333333; background: #FFFFFF;">Whitehead manifold</li> |
| - | <li>Lamplighter groups</li> | + | <li style="color: #333333; background: #FFFFFF;">Lamplighter groups</li> |
| - | <li> Heegaard splittings</li> | + | <li style="color: #333333; background: #FFFFFF;"> Heegaard splittings</li> |
| - | <li> Legendrian knots (definition and classical invariants) </li> | + | <li style="color: #333333; background: #FFFFFF;"> Legendrian knots (definition and classical invariants) </li> |
| - | <li>Find an unsolved problem in Adams' <i>The Knot Book</i> and explain work that's been done on it</li> | + | <li style="color: #333333; background: #FFFFFF;">Find an unsolved problem in Adams' <i>The Knot Book</i> and explain work that's been done on it</li> |
| </ul></p> | </ul></p> | ||
| <p><h3>Intermediate</h3> | <p><h3>Intermediate</h3> | ||
| <ul> | <ul> | ||
| - | <li> Trisections </li> | + | <li style="color: #333333; background: #FFFFFF;"> Trisections </li> |
| - | <li> Symplectic and/or contact manifolds</li> | + | <li style="color: #333333; background: #FFFFFF;"> Symplectic and/or contact manifolds</li> |
| - | <li>"Unusual" uses of Sard's theorem</li> | + | <li style="color: #333333; background: #FFFFFF;">"Unusual" uses of Sard's theorem</li> |
| <ul><li>e.g. in Gauss-Gersten-Stallings proof of the fundamental thm of algebra</li></ul> | <ul><li>e.g. in Gauss-Gersten-Stallings proof of the fundamental thm of algebra</li></ul> | ||
| - | <li>Four color theorem</li> | + | <li style="color: #333333; background: #FFFFFF;">Four color theorem</li> |
| <ul><li>Explain main ideas of proof, e.g. "discharging"</li> | <ul><li>Explain main ideas of proof, e.g. "discharging"</li> | ||
| <li>Relation to Lie algebras</li></ul> | <li>Relation to Lie algebras</li></ul> | ||
| - | <li>Yang-Baxter equation</li> | + | <li style="color: #333333; background: #FFFFFF;">Yang-Baxter equation</li> |
| - | <li>Use Conway notation to classify Euclidean 2-orbifolds/wallpaper groups</li> | + | <li style="color: #333333; background: #FFFFFF;">Use Conway notation to classify Euclidean 2-orbifolds/wallpaper groups</li> |
| - | <li>Circle packings and Andreev's theorem</li> | + | <li style="color: #333333; background: #FFFFFF;">Circle packings and Andreev's theorem</li> |
| - | <li>Lickorish Twist theorem</li> | + | <li style="color: #333333; background: #FFFFFF;">Lickorish Twist theorem</li> |
| - | <li>Isometric embeddings of the hyperbolic plane into R^3</li> | + | <li style="color: #333333; background: #FFFFFF;">Isometric embeddings of the hyperbolic plane into R^3</li> |
| - | <li>Topological proofs of Kneser's Conjecture and/or Grusko's Theorem</li> | + | <li style="color: #333333; background: #FFFFFF;">Topological proofs of Kneser's Conjecture and/or Grusko's Theorem</li> |
| - | <li>Rubinstein-Thompson 3-sphere recognition algorithm</li> | + | <li style="color: #333333; background: #FFFFFF;">Rubinstein-Thompson 3-sphere recognition algorithm</li> |
| - | <li>Essential surfaces in knot complements take only finitely many boundary slopes</li> | + | <li style="color: #333333; background: #FFFFFF;">Essential surfaces in knot complements take only finitely many boundary slopes</li> |
| - | <li>Classification of Lens Spaces</li> | + | <li style="color: #333333; background: #FFFFFF;">Classification of Lens Spaces</li> |
| - | <li>An Overview of the Eight 3-dimensional Geometries</li> | + | <li style="color: #333333; background: #FFFFFF;">An Overview of the Eight 3-dimensional Geometries</li> |
| - | <li>Interesting unknot diagrams and the unknotting problem</li> | + | <li style="color: #333333; background: #FFFFFF;">Interesting unknot diagrams and the unknotting problem</li> |
| - | <li>Brown's algorithm for the BNS invariant of two generator one relator groups</li> | + | <li style="color: #333333; background: #FFFFFF;">Brown's algorithm for the BNS invariant of two generator one relator groups</li> |
| - | <li>Finite type invariants of knots and 3-manifolds</li> | + | <li style="color: #333333; background: #FFFFFF;">Finite type invariants of knots and 3-manifolds</li> |
| - | <li>Dehn's problems and word-hyperbolic groups</li> | + | <li style="color: #333333; background: #FFFFFF;">Dehn's problems and word-hyperbolic groups</li> |
| - | <li>Recognizing hyperbolic 3-manifolds via SnapPea</li> | + | <li style="color: #333333; background: #FFFFFF;">Recognizing hyperbolic 3-manifolds via SnapPea</li> |
| - | <li>The curve complex and distances of Heegaard splittings</li> | + | <li style="color: #333333; background: #FFFFFF;">The curve complex and distances of Heegaard splittings</li> |
| - | <li>Pick a topic from Lickorish's or Rolfsen's book on knot theory and discuss related solved and unsolved problems.</li> | + | <li style="color: #333333; background: #FFFFFF;">Pick a topic from Lickorish's or Rolfsen's book on knot theory and discuss related solved and unsolved problems.</li> |
| - | <li>Survey of results on knotted and linked spheres in higher dimensions</li> | + | <li style="color: #333333; background: #FFFFFF;">Survey of results on knotted and linked spheres in higher dimensions</li> |
| <ul> | <ul> | ||
| <li><i>A sample of results</i>:</li> | <li><i>A sample of results</i>:</li> | ||
| Line 107: | Line 105: | ||
| <li>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.</li> | <li>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.</li> | ||
| </ul> | </ul> | ||
| - | <li>4-dimensional Schoenflies problem</li> | + | <li style="color: #333333; background: #FFFFFF;">4-dimensional Schoenflies problem</li> |
| - | <li>Quantum algorithms and the Jones polynomial</li> | + | <li style="color: #333333; background: #FFFFFF;">Quantum algorithms and the Jones polynomial</li> |
| - | <li>Equivariant versions of loop and sphere theorems</li> | + | <li style="color: #333333; background: #FFFFFF;">Equivariant versions of loop and sphere theorems</li> |
| </ul></p> | </ul></p> | ||
| <p><h2>Advanced</h2> | <p><h2>Advanced</h2> | ||
| <ul> | <ul> | ||
| - | <li> Choose an unsolved problem on the Kirby problem list and explain the most recent progress on that problem.</li> | + | <li style="color: #333333; background: #FFFFFF;"> Choose an unsolved problem on the Kirby problem list and explain the most recent progress on that problem.</li> |
| - | <li>Double suspension of the Mazur homology 3-sphere is the 5-sphere</li> | + | <li style="color: #333333; background: #FFFFFF;">Double suspension of the Mazur homology 3-sphere is the 5-sphere</li> |
| <ul> | <ul> | ||
| <li><i>Suggested reference</i>: Daverman, Robert J. Decompositions of manifolds. Pure and Applied Mathematics, 124. Academic Press, Inc., Orlando, FL, 1986. xii+317 pp. ISBN: 0-12-204220-4 </li> | <li><i>Suggested reference</i>: Daverman, Robert J. Decompositions of manifolds. Pure and Applied Mathematics, 124. Academic Press, Inc., Orlando, FL, 1986. xii+317 pp. ISBN: 0-12-204220-4 </li> | ||
| </ul> | </ul> | ||
| - | <li>Milnor's exotic 7-spheres</li> | + | <li style="color: #333333; background: #FFFFFF;">Milnor's exotic 7-spheres</li> |
| <ul> | <ul> | ||
| <li><i>Suggested reference</i>: Milnor, J., Differential topology. 1964, Lectures on Modern Mathematics, Vol. II pp. 165--183 | <li><i>Suggested reference</i>: Milnor, J., Differential topology. 1964, Lectures on Modern Mathematics, Vol. II pp. 165--183 | ||
| Wiley, New York (expository article)</li> | Wiley, New York (expository article)</li> | ||
| </ul> | </ul> | ||
| - | <li>Thurston's compactification of Teichmuller space</li> | + | <li style="color: #333333; background: #FFFFFF;">Thurston's compactification of Teichmuller space</li> |
| - | <li>Smales's proof of higher-dimensional Poincare Conjecture</li> | + | <li style="color: #333333; background: #FFFFFF;">Smales's proof of higher-dimensional Poincare Conjecture</li> |
| - | <li>Perelman's proof of the 3D Poincare Conjecture via Ricci flow</li> | + | <li style="color: #333333; background: #FFFFFF;">Perelman's proof of the 3D Poincare Conjecture via Ricci flow</li> |
| <ul> | <ul> | ||
| <li><i>Suggested reference</i>:Morgan, John W., Recent progress on the Poincare conjecture and the classification of 3-manifolds. Bulletin Amer. Math. Soc. 42 (2005) no. 1, 57-78</li> | <li><i>Suggested reference</i>:Morgan, John W., Recent progress on the Poincare conjecture and the classification of 3-manifolds. Bulletin Amer. Math. Soc. 42 (2005) no. 1, 57-78</li> | ||
| </ul> | </ul> | ||
| - | <li>Heegaard Floer homology</li> | + | <li style="color: #333333; background: #FFFFFF;">Heegaard Floer homology</li> |
| - | <li>Casson invariant</li> | + | <li style="color: #333333; background: #FFFFFF;">Casson invariant</li> |
| - | <li>Volume Conjectures</li> | + | <li style="color: #333333; background: #FFFFFF;">Volume Conjectures</li> |
| <ul> | <ul> | ||
| <li>Is Weeks manifold the smallest closed hyperbolic 3-manifold?</li> | <li>Is Weeks manifold the smallest closed hyperbolic 3-manifold?</li> | ||
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| <p><h2>Previous Talks</h2> | <p><h2>Previous Talks</h2> | ||
| + | |||
| + | <p><h3>Winter 2026</h3> | ||
| + | <p>Jan 5: Trevor Oliveira-Smith: "Extending Singular Fibrations of 3-manifolds"</p> | ||
| + | <p>Jan 12: Trevor Oliveira-Smith: "Intro to Sutured Manifolds" </p> | ||
| + | <p>Jan 19: MLK Day (no seminar)</p> | ||
| + | <p>Jan 26: Zach Ibarra: "Characterizations of Connections over the Field of Algebraic Numbers" </p> | ||
| + | <p>Feb 2: Trevor Oliveira-Smith: "Dehn Surgery and RBG-links" </p> | ||
| + | <p>Feb 9: Alex Simons "Lagrangian Cobordisms and Functoriality of the Legendrian Contact DGA"</p> | ||
| + | <p>Feb 16: President's Day (no seminar)</p> | ||
| + | <p>Feb 23: Cindy Zhang: "The h-cobordism theorem"</p> | ||
| + | <p>Mar 2: Ian Sullivan "Khovanov Homology's Kirby Object"</p> | ||
| + | <p> Mar 9: CANCELLED due to sick speaker</p> | ||
| + | |||
| <p><h3>Fall 2025</h3> | <p><h3>Fall 2025</h3> | ||
srtop.1770090840.txt.gz · Last modified: 2026/02/02 19:54 by asimons
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