Simon Brendle Dissertation Titles

References

  • C. BöHm and B. Wilking, Manifolds with positive curvature operator are space forms, Ann. of Math. (2) 167 (2008), 1079--1097.

    Mathematical Reviews (MathSciNet): MR2415394
    Digital Object Identifier: doi:10.4007/annals.2008.167.1079
    Zentralblatt MATH: 05578712

  • S. Brendle and R. Schoen, Manifolds with $1/4$-pinched curvature are space forms, to appear in J. Amer. Math. Soc., preprint,\arxiv0705.0766v3[math.DG]

    Mathematical Reviews (MathSciNet): MR2449060
    Digital Object Identifier: doi:10.1090/S0894-0347-08-00613-9

  • R. S. Hamilton, Three-manifolds with positive Ricci curvature, J. Differential Geom. 17 (1982), 255--306.

    Mathematical Reviews (MathSciNet): MR0664497
    Project Euclid: euclid.jdg/1214436922
    Zentralblatt MATH: 0504.53034

  • —, Four-manifolds with positive curvature operator, J. Differential Geom. 24 (1986), 153--179.

    Mathematical Reviews (MathSciNet): MR0862046
    Project Euclid: euclid.jdg/1214440433
    Zentralblatt MATH: 0628.53042

  • —, Four-manifolds with positive isotropic curvature, Comm. Anal. Geom. 5 (1997), 1--92.

    Mathematical Reviews (MathSciNet): MR1456308
    Zentralblatt MATH: 0892.53018

  • M. J. Micallef and J. D. Moore, Minimal two-spheres and the topology of manifolds with positive curvature on totally isotropic two-planes, Ann. of Math. (2) 127 (1988), 199--227.

    Mathematical Reviews (MathSciNet): MR0924677
    Digital Object Identifier: doi:10.2307/1971420
    JSTOR: links.jstor.org

  • M. J. Micallef and M. Y. Wang, Metrics with nonnegative isotropic curvature, Duke Math. J. 72 (1993), 649--672.

    Mathematical Reviews (MathSciNet): MR1253619
    Digital Object Identifier: doi:10.1215/S0012-7094-93-07224-9
    Project Euclid: euclid.dmj/1077289625
    Zentralblatt MATH: 0804.53058

  • H. Nguyen, Invariant curvature cones and the Ricci flow, Ph.D. dissertation, Australian National University, Canberra, 2007.

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Jun Shin, Editor

Jun Shin is a freshman in high school. He enjoys competition math as well as math research, and hopes to make USAJMO in 2018. He is most interested in algebra and number theory. Other than math, Jun likes to play basketball and take naps.

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Madeline Watts, Editor

Madeline Watts is currently a junior at a high school near Boulder, Colorado.  She enjoys all types of math and especially physics and algebra. She is a voracious reader and enjoys playing the saxophone, guitar, and piano. She is a varsity athlete on the cross country and track team. She wishes to pursue a career in architectural engineering or economics.

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Ayush Agarwal, Editor

Ayush Agarwal is a senior at Dougherty Valley High School who is a USAMO qualifier and USACO Platinum Contestant. An avid mathematician, researcher, and programmer, he spends most of his time working on challenging computational problems. He wants to help spread his passion for math to the community in any way he can: from summer math bootcamps, founding an international math circle, to private tutoring.

Professional editors:

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Stacy DeRuiter, Ph.D. Biological Oceanography, MIT (2008)

Stacy DeRuiter earned her bachelors degree in biology from St. Olaf’s College and in 2008 earned her Ph.D from MIT in biological oceanography. She has held many positions but is currently a professor of mathematics and statistics at Calvin College where she works as a statistical ecologist. Her research focuses on using math and statistics to analyze the behavior of whales and dolphins.

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Ed Aboufadel, Ph.D. Mathematics, Rutgers University (1992)

Ed earned his Ph.D in mathematics from Rutgers University in 1992. Since then he has served as a Professor of mathematics at Grand Valley State University, the Department chair of the Mathematics department, and he currently is serving as Assistant Vice President of Academic Affairs at the university. He has a wide variety of research interests spanning from wavelets, 3d printing, big data analytics, and 3d printing.

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Nic Brody, Masters student at UC Santa Barbara 

Nic Brody is currently a graduate student in the math department at UC Berkeley, where he studies geometric group theory and low-dimensional topology. He previously obtained a Master’s degree at UC Santa Barbara; his Master’s thesis was titled Limit Roots of Lorentzian Coxeter Groups.

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Nicholas Edelen, Ph.D. Mathematics, Stanford (2016)

Nicholas Edelen recently received his Ph.D. from Stanford under Simon Brendle, his dissertation bore the title On the free-boundary mean curvature flow.  He currently is a NSF Postdoctoral Fellow and works as an Instructor in Mathematics at MIT where his main research interest is differential geometry.

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Daniel Alvarez-Gavela, Ph.D. Candidate at Stanford

Daniel Alvarez-Gavela is a 4th-year graduate student at Stanford University under Yasha Eliasberg. He is studying the topology of manifolds. He earned his Bachelors degree from the University of Madrid. You can view his website here.

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Michael Bolt, Ph.D. Mathematics, University of Chicago

Michael Bolt is a Professor of Mathematics at Calvin College in Michigan where he has worked since 2004. He completed his Ph.D. at the University of Chicago in 2001 and has also held a position at the University of Michigan. Michael’s main interests are in Complex Analysis and in advising research projects for undergraduates.

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Muhammad Hamza Waseem, B.S. Electrical Engineering, UET

Muhammad Hamza Waseem is pursuing a BS Electrical Engineering at the University of Engineering and Technology (UET), Lahore, Pakistan. He is actively involved in science outreach and edits various high school and undergraduate science magazines and journals. Currently, he is investigating Fourier optics and holography.

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