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Math @ Duke





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Richard T. Durrett, James B. Duke Professor and Director of Graduate Studies

Richard T. Durrett
Contact Info:
Office Location:  117 Physics Building, Box 90320, Durham, NC 27708-0320
Office Phone:  (919) 660-6970
Email Address: send me a message
Web Page:  http://www.math.duke.edu/~rtd/

Teaching (Fall 2016):

  • MATH 340.01, ADVANCED INTRO PROBABILITY Synopsis
    Gross Hall 318, MW 10:05 AM-11:20 AM
    (also cross-listed as STA 231.01)
Education:

Ph.D.Stanford University1976
MSEmory University1973
BSEmory University1972
Specialties:

Probability
Research Interests:

Probability problems that arise from genetics and ecology, especially stochastic spatial models and cancer models. Random graphs and processes that take place on them.

Keywords:

Mathematical Concepts • Models, Biological • Models, Statistical • Models, Theoretical • Population Dynamics • Probability

Curriculum Vitae
Current Ph.D. Students   (Former Students)

  • Chris Varghese  
  • Junchi Li  
  • Yuan Zhang  
Postdocs Mentored

  • Anirban Basak (2014 - present)  
  • Marc Ryser (January, 2012 - present)  
  • David Herzog (2011-2014)  
  • Andreas Aristotelous (2011-2014)  
  • David Sivakoff (2010-2012)  
  • John Mayberry (2008 - 2010)  
  • Soumik Pal (2006 - 2008)  
  • Lea Popovic (2005 - 2007)  
  • Paul Jung (2003 - 2007)  
  • Iljana Zahle (2002 - 2003)  
  • Jason Schweinsberg (2001 - 2004)  
  • Vlada Limic (2000 - 2003)  
Undergraduate Research Supervised

  • Michael Lin (Summer 2014)
    He studied a four species evolutionary game that had previously been studied by Basanta, Scott, Rockne, Sanson and Anderson. He made good progress at mapping out the phase diagram, showing that some of the results in the paper were not correct. 
  • Luxi Wei (Fall 2013- Spring 2014)
    In the Fall of 2013, she read papers on modeling credit risk in preparation for writing a senior thesis, which she completed in the Spring of 2014. She graduated with distinction at the end of that semester. 
  • Anne Talkington (Summer 2013 - Summer 2016)
    In the summer of 2013 she studied models for cancer growth as part of the math biology RTG. During the 2013-2014 academic year we developed the research into a paper that has recently been accepted by the Bulletin of Mathematical Biology. She will graduate at the end of the Fall 2015 term but will stay around to do research with me in the Spring. 
  • Kaveh Danesh (2011-2013)
    In a collaboration with Evan Myers and Laura Havrilesky in the Duke Medical school, we worked on predicting the window of opportunity for ovarian cancer screening, resulting in a paper in J. Theor. Biol. Kaveh was a Fulbright Scholar studying cancer villages in China during 2013-2014, and is now in the Applied Math program. Since he is a student trustee I see him three times a year when they meet. 
  • Yifei Chen (Summer 2011)
    Participant in math bio RTG. His simulations were useful in improving a reuslt in my paper on population genetics of exponentially growing populations. 
  • Aashiq Dheeraj (2012-2013, Spring 2014)
    Math Bio RTG participant. Studied spatial versions of evolutionary game models in cancer. In the Spring of 2014 he wrote up this work as an honors thesis and graduated with distinction. 
  • Conrad de Peuter (Spring 2013)
    His honors thesis was "Using Markov renewal processes to model basketball games." He went to work at ESPN after graduation but later learned that a job that involve watching lots of basketball was not the dream it sounded like. He is now applying to graduate school in statistics. 
  • Willie Zheng (Spring 2013)
    Supervised his honors thesis in Math. Upon graduation he enrolled in an MD/PhD program at Washington U. St. Louis. 
Representative Publications   (More Publications)

  1. AC Aristotelous and R Durrett, Chemical evolutionary games., Theoretical population biology, vol. 93 (May, Submitted, 2014), pp. 1-13, ISSN 0040-5809 [doi]  [abs]
  2. F Shi, PJ Mucha and R Durrett, Multiopinion coevolving voter model with infinitely many phase transitions, Physical Review E, vol. 88 no. 6 (December, Accepted, 2013), ISSN 1539-3755 [doi]
  3. R. Durrett and S. Moseley, Spatial Moran Models. I. Tunneling in the Neutral Case, Annals Applied Probability (Accepted, 2013)
  4. C Varghese and R Durrett, Phase transitions in the quadratic contact process on complex networks, Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, vol. 87 no. 6 (2013), pp. paper 062819, ISSN 1539-3755 [doi]  [abs]
  5. K Danesh, R Durrett, LJ Havrilesky and E Myers, A branching process model of ovarian cancer., J Theor Biol, vol. 314 (2013), pp. 10-15 [22959913], [doi]  [abs]
  6. R Durrett, JP Gleeson, AL Lloyd, PJ Mucha, F Shi, D Sivakoff, JE Socolar and C Varghese, Graph fission in an evolving voter model., Proc Natl Acad Sci U S A, vol. 109 no. 10 (March, 2012), pp. 3682-3687 [22355142], [doi]  [abs]
  7. R. Durrett, Phase transition in a meta-population version of Schelling's model (Submitted, 2012)
  8. R. Durrett, J. Foo, and K. Leder, Spatial Moran Models II. Tumor growth and progression (Submitted, 2012)
  9. R Durrett and D Remenik, Evolution of dispersal distance, Journal of Mathematical Biology, vol. 64 no. 4 (2012), pp. 657-666, ISSN 0303-6812 [doi]  [abs]
  10. S Chatterjee and R Durrett, Asymptotic behavior of Aldous' gossip process, Annals of Applied Probability, vol. 21 no. 6 (2011), pp. 2447-2482, ISSN 1050-5164 [math.PR/1005.1608], [doi]  [abs]
  11. R Durrett, Population genetics of neutral mutations in exponentially growing cancer cell populations, Annals of Applied Probability, vol. 23 (2012), pp. 230-250
  12. JT Cox, R Durrett and E Perkins, Voter model perturbations and reaction diffusion equations, Asterique, vol. 349 (2013), pp. 1-113 [math.PR/1103.1676]
  13. R Durrett, J Foo, K Leder, J Mayberry and F Michor, Intratumor heterogeneity in evolutionary models of tumor progression, Genetics, vol. 188 no. 2 (2011), pp. 461-477, ISSN 0016-6731 [doi]  [abs]
  14. R Durrett and S Moseley, Evolution of resistance and progression to disease during clonal expansion of cancer, Theoretical Population Biology, vol. 77 no. 1 (2010), pp. 42-48, ISSN 0040-5809 [doi]  [abs]
  15. R Durrett, J Foo, K Leder, J Mayberry and F Michor, Evolutionary dynamics of tumor progression with random fitness values, Theoretical Population Biology, vol. 78 no. 1 (2010), pp. 54-66, ISSN 0040-5809 [math.PR/1003.1927], [doi]  [abs]
  16. R Durrett, SPecial invited paper coexistence in stochastic spatial models, Annals of Applied Probability, vol. 19 no. 2 (2009), pp. 477-496, ISSN 1050-5164 [MR2521876 (2010g:60213)], [doi]  [abs]
  17. R Durrett and D Schmidt, Waiting for two mutations: With applications to regulatory sequence evolution and the limits of Darwinian evolution, Genetics, vol. 180 no. 3 (2008), pp. 1501-1509, ISSN 0016-6731 [doi]  [abs]
Selected Invited Lectures

  1. IMS Wald Lectures, 2008    
  2. Medallion Lecture SPA Paris, 2006    
  3. St Flour Probability Summer School, 1993    
  4. International Congress of Math, 1990, Kyoto    
Recent Grant Support

  • Mathematical Analysis of Spatial Cancer Models, National Science Foundation, 1614838, 2016/07-2019/06.      
  • The Mathematics of Breast Cancer Overtreatment: Improving Treatment Choice through Effective Communication of Personalized Cancer Risk, National Institutes of Health, 2016/09-2018/08.      
  • Interacting Particle Systems on Lattices and on Graphs, National Science Foundation, 1505215, 2015/08-2018/07.      
  • Stochastic Spatial Models: on Complex Networks, Coevolution, and Modeling Cancer, National Science Foundation, DMS 1331778, 2013/09-2015/08.      
  • Biodiversity and Evolution - Support for US Participants, National Science Foundation, DMS 1305997, 2013/09-2015/08.      
  • Mathematical Models of Cancer Initiation, Progression, and Resistance to Therapy, National Institutes of Health, 7R01GM096190-02, 2010/07-2015/06.      
Conferences Organized

 

dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821

Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320