Peter D. Hislop
  Professor of Mathematics
  Ralph E. and Norma L. Edwards Research Professor of Mathematics, 2010-2013
  University Research Professor, 2004-2005
 

E-Mail:

    hislop@ms.uky.edu or peter.hislop@uky.edu

Phone Numbers:
 

  Office: 
  FAX: 

+1 859 257 5637
+1 859 257 4078 
Peter D. Hislop

Mailing Address:

    Department of Mathematics
    University of Kentucky
    753 Patterson Office Tower
    Lexington, Kentucky  40506-0027

Recent Research Papers:

My recent research has focussed on three areas: random Schrodinger operators, geometric analysis of real and complex hyperbolic manifolds, and resonance and eigenvalue estimates. My research is partially supported by the National Science Foundation DMS. My current doctoral students are Megan Gier and Aaron Saxton. You can also check the archives for most of my recent papers.

A more complete list of my publications may be found on MathSciNet.

Upcoming Workshops:

Five-day workshop at the Banff International Research Station in Banff, Canada: Geometric scattering theory, co-organized with F. Froese, R. Mazzeo, and P. Perry, 2 - 7 November 2014.

Ohio River Analysis Meeting 4, University of Kentucky, Saturday and Sunday, 8-9 March 2014.

Course Material for Spring 2014:

This course will cover the basics of Riemannian geometry following the book Riemannian geometry by do Carmo (Birkhauser, 1988). We will study differentiable manifolds, Riemannian metrics, tangent and cotangent spaces, vector fields, geodesics, connections, and curvature. We will develop enough machinery to describe the spaces of constant curvature and complete manifolds. Riemannian geometry is built on the classical theory of curves and surfaces in space. It is recommended that the students look at a book such as Differential geometry of curves and surfaces by do Carmo to see the origins of the subject. NEW: Classroom change to CB 341!!

This is the first semester of calculus. After a review of functions, we will study the derivative and integral. ALL FOUR SECTIONS MEET FOR LECTURES: MWF 12:00-12:50 in CB 114. .

Course Material for Fall 2013:

This is a course in Banach and Hilbert space theory with an emphasis on the theory of linear operators. The class meets MWF 12-12:50 in CB 343. Special class: Monday, 7 October at 4PM

This is the first semester of calculus. After a review of functions, we will study the derivative and integral. ALL FOUR SECTIONS MEET FOR LECTURES: MWF 2:00-2:50 in CB 110. The book store may still have some copies of the book. You can also order it on Amazon. NEW: Final exam, Wednesday, 18 December, 8:30--10:30 PM in CB 118. REVIEW SESSION: Tuesday, 17 December 2013 3:30-5 PM in CB 118. Good luck with the final!

Course Material for Spring 2013:

    MA507 and PHY507 Mathematical Methods of Physics

    MA 114 Calculus II sections 005, 006, 007, 008

This is the second semester of calculus. We will study integration methods and applications. ALL FOUR SECTIONS MEET FOR LECTURES: MWF 10:00-10:50 in CP 320. NEW: Final Review: Sunday and Monday, 28 and 29 April, from 6:30-8:30 PM, in CP 153 (Sunday) and CB 102 (Monday). Final Exam, 1 May, 6-8 PM in BS 107. Alternate Final Exam, 2 May, 1-3 PM in the Mathskellar. Good luck! Room for Final Exam: BS 107 (Biological Sciences).

Course Material for Fall 2012:

    MA506 and PHY506 Mathematical Methods of Physics

Course Material for Spring 2012:

    MA 633 001 Partial Differential Equations II

  • Midterm exam on Friday, 23 March, over the material in Chapter 5.

Course Material for Fall 2011:

    MA 533 001 Partial Differential Equations

    MA 113 Sections 029, 030, 031, and 032 Calculus 1

This is the basic course in the calculus of functions of one real variable. The emphasis of Calculus 1 is differentiation, integration and applications. MEETS: MWF 12:00-12:50 in BE 148.

Final Exam on Wednesday, 14 December, 6:00-8:00 PM in the Student Center Theater. Review session: Monday, 12 December, 6:00-8:00 PM Room 110 CB.

Exam 3 is on Tuesday, 15 November, 7:30-9:30 PM, in the Student Center Theater. REVIEW SESSION: Monday, 14 November, 7:30 PM in Room CB 106 (Note change of room from last time).

Course Material for Spring 2011:

    Possible paper topics:

    Ricci flow and the Poincare conjecture (book by Morgan and Tian), see also "Recent progress on the Poincaré conjecture and the classification of 3-manifolds," J. Morgan, BAMS, (2005). "Towards the Poincaré conjecture and the classification of 3-manifolds," J. Milnor, Notices AMS, 2003.

    MA 214 Section 002 Ordinary Differential Equations:

This is a basic course on ordinary differential equations (ODEs). There are three main components: 1) first-order ODEs and modeling (chapter 1-2), 2) second-order ODEs and applications to oscillators (chapter 3), and 3) the Laplace transform and applications to initial value problems.

The final grades are posted. Good luck with everything and have a good summer! you can get copies of your final and the solutions are posted below.

  • Homework Problems
  • This course has a computer lab component using a free software package called IODE developed at the University of Illinois by P. Brinkmann, R. Jerrard, and R. Laugesen. There will be four projects during the semester. No prior knowledge of MatLab is needed. IODE also runs on GNU Octave, a free software available at: http://www.gnu.org/software/octave/. I have not used it but there are comments about using Octave on the Illinois Iode web page.

    You may now download IODE from the main IODE web page. The program works on 2007, 2008, 2009 and 2010 versions of Matlab. These are on the machines in Engineering and the library. The Save feature now works but it might still be more convenient to save your work as described next: ON SAVING GRAPHS: It is easiest to save your graphs as a Word document. This is convenient because you can put two graphs on one page and add comments! Enlarge the graph using the button on the upper right so it fills the screen. Press the "Print Screen" key on the keyboard. This copies the screen into a temp directory. Open Word and simply past the document into word. You can also type in your explanations, etc. you should then save the word document to your locker on the L-drive.

    Course Material for Fall 2010:

      MA 641 Differential Geometry

      This course will cover the basics of Riemannian geometry following the book Riemannian geometry by do Carmo (Birkhauser, 1988). We will study differentiable manifolds, Riemannian metrics, tangent and cotangent spaces, vector fields, geodesics, connections, and curvature. We will develop enough machinery to describe the spaces of constant curvature and complete manifolds. Riemannian geometry is built on the classical theory of curves and surfaces in space. It is recommended that the students look at a book such as Differential geometry of curves and surfaces by do Carmo to see the origins of the subject.

    Course Material for Spring 2010:

      MA 776 Pseudodifferential Operators and Applications:

      This course will be a self-contained course on pseudodifferential operators (PsDOs). The goal is to prove a theorem of Hormander on the asymptotic behavior of the eigenvalue counting function for an elliptic, lower-semibounded, self-adjoint PsDO on a compact Riemannian manifold. This will require us to study: oscillatory integrals, stationary phase, symbol calculus, basic properties of PsDOs (products, paramatrices), and basic Fourier integral operators.

      MA 214 Section 003 Ordinary Differential Equations:

    This is a basic course on ordinary differential equations (ODEs). There are three main components: 1) first-order ODEs and modeling (chapter 1-2), 2) second-order ODEs and applications to oscillators (chapter 3), and 3) the Laplace transform and applications to initial value problems.

    NEW: Grades are posted. You may get a copy of your final by stopping by my office. The solutions are posted below. Have a good summer!

    This course has a computer lab component using a free software package called IODE developed at the University of Illinois by P. Brinkmann, R. Jerrard, and R. Laugesen. There will be four projects during the semester. No prior knowledge of MatLab is needed. IODE also runs on GNU Octave, a free software available at: http://www.gnu.org/software/octave/. I have not used it but there are comments about using Octave on the Illinois Iode web page.

    You may now download IODE from the main IODE web page. The program works on 2007, 2008 and 2009 versions of Matlab. The Save feature now works but it might still be more convenient to save your work as described next: UPDATE on SAVING GRAPHS: If the usual save button does not work, you can save to a Word document. This is convenient because you can put two graphs on one page and add comments! Enlarge the graph using the button on the upper right so it fills the screen. Press the "Print Screen" key on the keyboard. This copies the screen into a temp directory. Open Word and simply past the document into word. You can also type in your explanations, etc.

  • Course Syllabus for MA214 003, Spring 2010

  • Instructions on how to start-up IODE using Matlab, Spring 2010

  • A Brief Guide to Matlab Syntax

  • Open Lab Hours in CB313, Spring 2010. I will hold my office hour in CB 313 on Wednesdays 4-5 PM. We can discuss the labs and homework.

  • Lab 1: Introduction to IODE and the first project, Spring 2010

  • Project 1: Due in class, Friday, 5 February 2010. You can use MatLab in the RG Anderson building computer labs, in the Science and Engineering Library lab (King South), and in CB 313 during open lab hours (schedule to be posted.) You cannot print in CB 313 so save your graphs in your locker using word, for example, and print them in another lab.

  • Comments on Project 1 compiled from reading the project reports. Please read through these comments and think about them as you do Project 2. GRADING: The lab was worth 15 points: the first ODE 3 points, and the remaining 3 ODEs were worth 4 points.

  • Project 2: Due in class, Wednesday, 3 March 2010.

  • Comments on Project 2 compiled from reading the project reports. Please read through these comments and think about them as you do Projects 3 and 4. GRADING: The lab was worth 15 points.

  • Project 3: Due in class, Monday, 29 March 2010.

  • Project 4: Due in class, Friday, 23 April 2010.

  • Notes on Exponentials, Logs, and Complex Numbers

  • Homework Problems
  • Quiz 1 Solutions
  • Quiz 2 Solutions
  • Practice Test #1
  • Test #1 solutions. (Correction: In Problem 5, the value of y_2 is 2.)
  • Quiz 3 Solutions
  • Quiz 4 Solutions
  • Practice Test #2
  • Test #2 solutions.
  • Table of formulas for Laplace transforms. This table will always be available to you during quizzes and the final exam.
  • Quiz 5 Solutions
  • Quiz 6 Solutions
  • Practice Final Exam.
  • Solutions to the Final Exam Spring 2010.
  • Course Material for Fall 2009:

      MA 677 Real Analysis II:

      This course is a continuation of Reals I taught in the spring of 2009. We will continue with the book of Stein and Shakarchi. You should be reading Chapter 6 on abstract measure theory. You should also be focussing on your paper and projects. Please see me to discuss them! A draft of you paper is due in class on 18 November 2009.

  • Course Syllabus for MA677, Fall 2009

  • Problem Set 1 due 9 September 2009.
  • Problem Set 2 due 2 October 2009.
  • Problem Set 3 due 16 October 2009.
  • Problem Set 4 due 4 December 2009.
    • MA 214 Section 003 Ordinary Differential Equations:

    NO LAB OFFICE HOUR Wednesday, 9 Dec. 3-4. There will be a review session Tuesday, 15 December, at 3 PM in 316 CB. Office Hour on Monday, 14 December 11 AM-12 PM and 4-5 PM in my office, 753 POT. ALL GRADES ARE FINAL (except the final exam grade and the lab 3 grade) AT 4PM TODAY UNLESS YOU CONTACT ME.

    We have finished all the work for our course. In chapter 6, we did sections 6.1-6.5. We will begin to review for the final exam tomorrow, Wednesday. The final exam is scheduled for: Wednesday, 16 December, 10:30-12:30, in our classroom CB 203. It is worth 180 points. I will award everyone 15 points for the lab that we were not able to do. A practice exam is posted below and you may find other practice final exams posted in pervious versions of this course below (Remember: we did not do exact ODEs.)

    This course will have a lab component using a free software package called IODE developed at the University of Illinois by P. Brinkmann, R. Jerrard, and R. Laugesen. There will be four projects during the semester. No prior knowledge of MatLab is needed. IODE also runs on GNU Octave, a free software available at: http://www.gnu.org/software/octave/. I have not used it but there are comments about using Octave on the Illinois Iode web page.

    UPDATE: You may now download IODE from the main IODE web page. The program works on 2007, 2008 and 2009 versions of Matlab. The only feature that does not work is the Save feature. Save your work as described next: UPDATE on SAVING GRAPHS: If the usual save button does not work, you can save to a Word document. This is convenient because you can put two graphs on one page and add comments! Enlarge the graph using the bottom on the upper right so it fills the screen. Press the "Print Screen" key on the keyboard. This copies the screen into a temp directory. Open Word and simply past the document into word. You can also type in your explanations, etc. Third project due date Friday, 4 December, in class. Please staple your pages together! CHANGE: Open lab in CB 313 on Wed. 2 Dec. from 3:15 - 4:00 PM only! You may turn in your projects on Monday.

  • Course Syllabus for MA214, Fall 2009

  • Notes on Exponentials, Logs, and Complex Numbers

  • Open Lab Hours in CB313, Fall 2009 (Please note the change on T and R mornings!)

  • Instructions on how to start-up IODE using Matlab, Fall 2009

  • A Brief Guide to Matlab Syntax, Fall 2009

  • Lab 1: Introduction to IODE, Fall 2009

  • Project 1: NEW! due in class, Wednesday, 23 September 2009 (read above). Try to get to CB313. Save you graphs in your locker using word, for example, and print them in another lab.

  • Comments on Project 1 compiled from reading the project reports. Please read through these comments and think about them as you do Project 2. GRADING: I will add 5 points to your score on Project 1 since it should have been worth 15 points.

  • Comments on Project 2 compiled from reading the project reports. Please read through these comments and think about them as you do Project 3.

  • Project 2: Due in class, Friday, 30 October 2009.

  • Project 3: Due in class, Friday, 4 December 2009.

  • Homework Problems
  • Table of formulas for Laplace transforms.
  • Quiz 1 Solutions
  • Quiz 2 Solutions
  • Quiz 3 Solutions
  • Quiz 4 Solutions
  • Practice Test #1
  • Practice Test #1 solutions
  • Test #1 solutions (Correction: Problem 4(c): The answer is P_0, not P_0 e.)
  • Quiz 5 Solutions
  • Practice Test #2.
  • Practice Test #2 solutions
  • Test #2 solutions.
  • Quiz 6 Solutions
  • Practice Final Exam.
  • Solutions to the Final Exam Fall 2009.
  • Course Material for Spring 2009:

      MA 676 Real Analysis I:

  • The grades have been posted online and the solutions to the final are below. I will return the final exam and PS #7 to your mailboxes. Have a good summer!

  • WEEKLY PROBLEM SESSION on Wednesdays at 4PM in CB 341. We are doing chapter 6 on Laplace transforms. Read sections 6.1-6.5. No problem session on Wednesday, 29 April. We will be reviewing all week. A final exam review is scheduled for Thursday, 7 May, at 5:30PM, room CB 333.

  • Course grades will be posted today, Monday, 11 May. The solutions to the final are posted below. You may stop by anytime to look at your final. Have a good summer!

  • Course Syllabus

  • Homework Problems
  • Table of formulas for Laplace transforms.
  • Quiz 1 Solutions
  • Quiz 2 Solutions
  • Quiz 3 Solutions
  • Quiz 4 Solutions
  • Quiz 5 Solutions
  • Quiz 6 Solutions
  • Quiz 7 Solutions
  • Quiz 8 Solutions
  • Quiz 9 Solutions
  • Quiz 10 Solutions
  • Test #1 Solutions
  • Test #2 Solutions
  • Final Exam Solutions
  • Course Material for Fall 2008:

      MA 214 Section 03 Ordinary Differential Equations:

    • MA 575 Principles of Analysis:

  • UK Webpages:

  • Mathematics Department
  • College of Arts and Sciences
  • University of Kentucky