Research Interests Jeffrey Meier
Broadly, I am interested in knot theory, knotted surfaces, and the topology of 3-manifolds and 4-manifolds. In particular, I have a great interest in trisections of 4-manifolds; 4-dimensional knot theory, including fibered ribbon 2-knots, knotted Klein bottles and projective planes, surgery operations, and bridge trisections; various aspects of knot concordance, including doubly slice knots, fibered ribbon knots, cabled slice knots, and applications of knot homology theories; and Dehn surgery, especially exceptional surgery and Seifert fibered surgery.
- Cubic graphs induced by bridge trisections [arXiv] with Abigail Thompson and Alexander Zupan
- Symplectic 4-manifolds admit Weinstein trisections [arXiv] with Peter Lambert-Cole and Laura Starkston
- Branched covers bounding rational homology balls [arXiv] with Paolo Aceto, Allison N. Miller, Maggie Miller, JungHwan Park, and András I. Stipsicz
- Note on 3-fold branched covers of S3 [arXiv] with Ryan Blair, Patricia Cahn, and Alexandra Kjuchukova
- Null, recursively starlike-equivalent sets shrink [arXiv] with Patrick Orson and Arunima Ray
- Generalized square knots and homotopy 4-spheres [arXiv] with Alexander Zupan
To appear in Journal of Differential Geometry - Bridge trisections in rational surfaces [arXiv] with Peter Lambert-Cole
To appear in Journal of Topology and Analysis - Doubly pointed trisection diagrams and surgery on 2-knots [arXiv] with David Gay
- Trisections and spun 4-manifolds [arXiv]
Mathematical Research Letters 25(5) (2018), 1497 – 1524 - Bridge trisections of knotted surfaces in 4-manifolds [arXiv] with Alexander Zupan
Proceedings of the National Academy of Sciences 115(43) (2018), 10880-10886 - Characterizing Dehn surgery on links via trisections [arXiv] with Alexander Zupan
Procedings of the National Academy of Science 115(43) (2018), 10887-10893 - Bridge trisections of knotted surfaces in S4 [arXiv] with Alexander Zupan
Transactions of the AMS, Vol. 369 (2017), 7343-7386 - Genus two trisections are standard [arXiv] with Alexander Zupan
Geometry & Topology 21 (2017), 1583-1630 - A note on cabled slice knots and reducible surgeries [arXiv]
Michigan Mathematics Journal Vol. 66, Issue 2 (2017), 269-276 - Classifying trisections and the Generalized Property R Conjecture [arXiv] with Alexander Zupan and Trenton Schirmer -- Proceedings of the AMS, Vol. 144(11) (2016), 4983-4997
- Doubly slice knots with low crossing number [arXiv] with Charles Livingston
New York Journal of Mathematics, Vol. 21 (2015), 1007-1026 - Fibered ribbon disks [arXiv] with Kyle Larson
Journal of Knot Theory and Its Ramifications, Vol. 24 (2015), 1550066, pp. 22 - Distinguishing topologically and smoothly doubly slice knots [arXiv]
Journal of Topology 8 (2015), 315-351 - Small Seifert fibered surgery on hyperbolic pretzel knots [arXiv]
Algebraic & Geometric Topology 14 (2014), 439-487 - Isolation-by-distance and outbreeding depression are sufficient to drive parapatric speciation in the absence of environmental influences with René Doursat, Rich Drewes, and Guy Hoelzer
PLoS Computational Biology 4(7) (2008), 11 pp.
Videos and Slides
Here are some videos and slides from talks I've given.- Trisections and homotopy four-spheres [Dropbox]
- Tangles, 2-knots, and Trisections [Slides]
- Bridge trisections of surfaces in four-manifolds [Video (courtesy of CIRM)]
- Bridge trisections for knotted surfaces in the 4-sphere [Video (courtesy of BIRS), Slides]
- Trisecting the Gluck twist [Slides]
- Fibered Ribbon Disks [Slides]
- Seifert Fibered Surgery on Hyperbolic Montesinos Knots [Slides]
- Knots, Seifert Surfaces, and the Slice-Ribbon Conjecture [Video (courtesy of the UT Austin Math Club)]
Invited Talks
Below is a selection of invited talks I've given, along with links to some of the corresponding videos and slides.
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Homotopy 4-spheres [Dropbox]
- MIT Virtual Topology Seminar (May 2020)
- Virtual Trisections Meeting (April 2020)
- A Celebration of the Mathematics of Bob Gompf, The University of Texas at Austin (July 2018)
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Tangles, 2-knots, and Trisections [Slides]
- UnKnot IV, University of Washington Bothell (July, 2019)
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Bridge trisections of surfaces in four-manifolds [Video]
- Spring 2018 Redbud Conference, Oklahoma State University (April, 2018)
- Knotted Embeddings in Dimensions Three and Four, CIRM, Luminy-Marseille, France (February, 2018)
- Topology Seminar, University of Virginia (December 2017)
- Cascade Topology Seminar, University of Victoria, Canada (October 2017)
- Topology Seminar, University of California, Davis (October 2017)
- Topology Seminar, University of California, Berkeley (October 2017)
- Topology Seminar, University of Georgia (August 2017)
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Fibered homotopy-ribbon knots
- A Celebration of the Mathematics of Bob Gompf, The University of Texas at Austin (July 2018)
- Winter Braids VIII, CIRM, Luminy-Marseille, France (February 2018)
- Joint Topology Seminar, Georgia Tech University (September 2017)
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Relative bridge trisections
- Topology Seminar, North Carolina State University (March 2018)
- Topology Seminar, The University of Georgia (March 2017)
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Group trisections
- Max Plank Institute for Mathematics, Bonn, Germany (December 2016)
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Introduction to bridge trisections and knotted surfaces
- Mini-course, Southeastern Undergraduate Mathematics Workshop (August 2017)
- Department Colloquium, Utah State University (January 2017)
- Learning seminar on trisection theory [Schedule]
- Junior Trimester in Topology, Hausdorff Institute for Mathematics, Bonn, Germany (Fall 2016)
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Trisecting the Gluck twist [Slides]
- Georgia Topology Conference, The University of Georgia (May 2016)
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Bridge trisections for knotted surfaces in the 4-sphere [Video, Slides]
- Trisections and Low-Dimensional Topology, American Institute of Mathematics (March 2017)
- Eastern Illinois Integrated Conference in Geometry, Dynamics, and Topology, Easter Illinois University (April 2016)
- 14th Graduate Student Topology and Geometry Conference, Indiana University (April 2016)
- Synchronizing Smooth and Topological 4-Manifolds, Banff International Research Station (February 2016)
- Topology Seminar, Princeton University (February 2016)
- Topology Seminar, Georgia Tech University (December 2015)
- Topology Seminar, Boston College (October 2015)
- Moab Topology Conference, Utah State University, Moab (May 2015)
- Topology Seminar, Oklahoma State University (April 2015)
- Topology Seminar, The University of Texas at Austin (March 2015)
- AMS Spring Central Sectional Meetings, Michigan State University (March 2015)
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Classifying trisections and the Generalized Property R Conjecture
- Topology Seminar, University of Nebraska, Lincoln (February 2016)
- Topology Seminar, The University of Texas at Austin (October 2015)
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Fibered Ribbon Disks [Slides]
- AMS Fall Western Sectional Meetings, San Francisco State University (October 2014)
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Distinguishing Topologically and Smoothly Doubly Slice Knots
- Topology Seminar, Caltech (April 2014)
- Topology Seminar, University of Virginia (April 2014)
- Topology Seminar, University of California, Davis (February 2014)
- Topology Seminar, Indiana University (November 2013)
- Topology Seminar, Univesrity of California, Santa Barbara (December 2013)
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A Quick Trip Through the History of Slice and Doubly Slice Knots
- Colloquium, University of Nevada, Reno (February 2014)
- Colloquium, Sam Houston State University (November 2013)
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Knots, Seifert Surfaces, and the Slice-Ribbon Conjecture [Video ]
- Math Club, University of Texas at Austin (February 2013)
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Seifert Fibered Surgery on Hyperbolic Montesinos Knots [Slides]
- Low-dimensional Topology and Geometry in Toulouse, Université Paul Sabatier (June 2013)
- AMS Spring Eastern Sectional Meetings, Boston College (April 2013)
- 10th Graduate Student Topology and Geometry Conference, Indiana University (April 2012)