E-mail: glivshyts6@math.gatech.edu

Address: Room 228, Skiles bldg, located at 686 Cherry street NW, Atlanta, GA, 30332.

- G. V. Livshyts, An extension of Minkowski's theorem and its applications to questions about projections for measures, to appear in Advances in Math.
- G. V. Livshyts, K. Tikhomirov, Randomized coverings of a convex body with its homothetic copies, and illumination, submitted.
- A. Colesanti, G. V. Livshyts, A. Marsiglietti, On the stability of Brunn-Minkowski type inequalities, Journal of Functional Analysis 273 (2017), no. 3, 1120-1139.
- G. Livshyts, A. Marsiglietti, P. Nayar, A. Zvavitch, On the Brunn-Minkowski inequality for general measures with applications to new isoperimetric type-inequalities, Transactions of the AMS, electronic version: April 11, 2017.
- G. Livshyts, P. Paouris, P. Pivovarov, On sharp bounds for marginal densities of product measures, Israel Journal of Mathematics, (2016), 216(2), 877-889.
- G. V. Livshyts, Surface area of polytopes with respect to log-concave rotation invariant measures, Adv. Appl. Math., vol. 70, 54-69, (2015).
- G. V. Livshyts, Maximal Surface Area of a convex set in Rn with respect to log concave rotation invariant measures, GAFA Seminar Notes, 2116, (2014), 355-384.
- G. V. Livshyts, Maximal surface area of a convex set in Rn with respect to exponential rotation invariant measures, J. Math. Anal. Appl., 404, 2, (2013), 231-238.

- A. Colesanti, G. V. Livshyts, The log-Minkowski problem in a Hausdorff neighborhood of a ball, in preparation for submission.
- G. V. Livshyts, K. Tikhomirov, Cube is a strict local maximizer for the illumination number, in preparation for submission.
- B. Jaye, G. V. Livshyts, G. Paouris, P. Pivovarov, Minimizing Renyi entropy of the sum of independent random vectors, in preparation.
- P. Ivanisvili, G. V. Livshyts, I. Popescu, C. Saroglou, On several approaches to the Log-Brunn-Minkowski inequality, in preparation.
- G. V. Livshyts, V. Yaskin, On convex bodies with polynomial section functions of arbitrary degrees, in preparation.
- G. V. Livshyts, On the Gaussian concentration inequality and its relation to the Gaussian surface area, a letter (not intended for publication).

### Probability II (Spring 2017, graduate)

#### Home work 2 (Probability II)

#### Home work 3 (Probability II)

### Probability I (Fall 2016, graduate)

#### Home work 1 (Probability I)

#### Home work 2 (Probability I)

#### Home work 3 (Probability I)

#### Home work 4 (Probability I)

#### Home work 5 (Probability I)

#### Test 1 (Probability I)

#### Test 2 (Probability I)

#### Midterm (Probability I)

### PUTNAM preparation (Fall 2016, undergraduate)

The William Lowell Putnam Mathematical Competition is an annual mathematics competition for undergraduate college students enrolled at institutions of higher learning in the United States and Canada. It awards a scholarship and cash prizes ranging from $250 to $2,500 for the top students and $5,000 to $25,000 for the top schools. It is widely considered to be the most prestigious university-level mathematics examination in the world. The competition was founded in 1927 by Elizabeth Lowell Putnam in memory of her husband William Lowell Putnam. The exam has been offered annually since 1938 and is administered by the Mathematical Association of America. See the oficial webpage of the PUTNAM competition, as well as the page containing PUTNAM problems and solutions of the recent years. All of the Georgia Tech students interested in participating PUTNAM, and/or joining my class aimed to prepare for the competition, which runs on Tuesdays 3:05-4:55 pm at 171 skiles, are more then welcome to get in touch with me via e-mail, or stop by my office 228 Skiles, or to just show up in class! Below please see some materials for the course.

#### PUTNAM exam 2015

#### Solutions to PUTNAM exam 2015

#### Excersize set 1 (PUTNAM preparation)

#### Problem set 1 (PUTNAM preparation)

#### Problem set 2 (PUTNAM preparation)

#### Problem set 3 (PUTNAM preparation)

#### Problem set 4 (PUTNAM preparation)

#### Mini olympiad (PUTNAM preparation)

#### Problem set 6 (PUTNAM preparation)

#### Problem set 7 (PUTNAM preparation)

#### Problem set 8 (PUTNAM preparation)

#### Problem set 9 (PUTNAM preparation)

#### Problem set 10 (PUTNAM preparation)

### Introduction to Probability and Statistics (Fall 2015, undergraduate)