Dr. Guenther presented her work the area of "renormalization group flow" at the University of Tennessee, Knoxville.

# Christine Guenther, PhD

### Course Information

At Pacific University, all faculty teach a variety of different courses. Typically, we do not use graduate teaching assistants, which means that your classes will be taught by professors and that you will have plenty of opportunities to get to know the faculty in your discipline.

Below I have listed some of the courses that I teach. We are always developing and trying out new classes, so the list may change now and then.

MATH 226 | Calculus I

MATH 227 | Calculus II

MATH 228 | Calculus III

MATH 240 | Discrete Mathematics

MATH 311 | Ordinary Differential Equations

MATH 321 | Higher Geometry

MATH 330 | Probability

MATH 326 | Introduction to Analysis

MATH 411 | Partial Differential Equations

MATH 490 | Senior Capstone

### Education

PhD in Mathematics, University of Oregon, Eugene, OR

MA in Mathematics, University of Washington, Seattle, WA

BS in Mathematics, BA in Music, Stanford University, Palo Alto, CA

### Published Works

E. Bahuaud, C. Guenther, J. Isenberg, R. Mazzeo, *Convergence stability for Ricci flow on manifolds with bounded geometry, *Proc. Amer. Math.Soc. **152 **no. 1 435-446, (2024)

E. Bahuaud, C. Guenther, J. Isenberg, R. Mazzeo, *Sectoriality of the Laplacian on Asymptotically Hyperbolic Spaces, *accepted for publication, Annals of Global Analysis and Geometry (2024)

B. Andrews, B. Chow, C. Guenther, M. Langford, “*Extrinsic Geometric Flows*”, pp. 1 – 750, American Mathematical Society, Graduate Studies in Mathematics, **206 **(2020)

M. Carfora, C. Guenther, “*Scaling and Entropy for the RG-2 Flow”*, Comm. Math. Phys **378 **(3) (2020)

E. Bahuaud, C. Guenther, J. Isenberg, “*Stability Convergence for Ricci Flow”, *J. Geom. Anal. (2019) https://doi.org/10.1007/s12220-018-00132-9

*Mean Curvature Flow. Proceedings of the John H. Barrett Memorial Lectures held at the University of Tennessee, Knoxville, May 29 - June 1, 2018*. Bourni, T., M. Langford (Ed.). Berlin, Boston: De Gruyter (2019) https://www.degruyter.com/view/product/509846

K. Gimre, C. Guenther, J. Isenberg, “*Short-time existence for the second order renormalization group flow in general dimensions*”, Proc. Am. Math. Soc., Vol 143, no. 10 (2015)

B. Chow, S-C Chu, D. Glickenstein, C. Guenther, J. Isenberg, T.Ivey, D.Knopf, F. Luo, L. Ni, *The Ricci Flow:Techniques and Applications. Part IV: Long-time Solutions and Related Topics*, Mathematical Surveys and Monographs, American Mathematical Society, Providence, R.I. (2015)

K. Gimre, C. Guenther, J. Isenberg, “*A geometric introduction to the two-loop renormalization group flow.*” J. Fixed Point Theory Appl. 14, (2013), Volume 14, Issue 1, pp 3-20

K. Gimre, C. Guenther, J. Isenberg*, Second-order Renormalization Group flow of three-dimensional homogeneous geometries*. Comm. Anal. Geom. 21 no. 2, (2013) 435-467.

K. Gimre, R. Whiteley, C. Guenther, *The Analytical Determination of Kinetic Parameters for a Bimolecular EC Mechanism from Chronoamperometric Data*, J. Math. Chem. **250** (2012), no. 4, 805 – 818

The Analytical Determination of Kinetic Parameters of Kinetic Parameters for a Bimolecular EC Mechanism from Chronoamperometric Data (Paper: with R. Whiteley, K. Gimre*), to appear in *Journal of Mathematical Chemistry* 2011.

Ricci Flow, Techniques and Applications. Part III: Geometric-Analytic Aspects (with Chow, B. Chu, S-C, Glickenstein, D., Isenberg, J., Ivey, T., Knopf, D., Luo, F., Ni, L.) *Mathematical Surveys and Monographs* 163, American Mathematical Society, Providence, R.I. (2010).

Stability of the (Two-Loop) Renormalization Group Flow for Nonlinear Sigma Models (with Oliynyk, T.), *Letters in Mathematical Physics*, Vol 84, No. 2, 149-157 (2008).

Ricci Flow, Techniques and Applications. Part II: Analytic Aspects (with Chow, B. Chu, S-C, Glickenstein, D., Isenberg, J., Ivey, T., Knopf, D., Luo, F., Ni, L.) *Mathematical Surveys and Monographs *144, American Mathematical Society, Providence, R.I. 2008.

Ricci Flow: Techniques and Applications. Part I. Geometric Aspects (with Chow, B., Chu, S-C, Glickenstein, D., Isenberg, J., D., Ivey, T., Knopf, Luo, F., Lu, P., Luo, F., Ni, L).* Mathematical Surveys and Monographs*, 135. American Mathematical Society, Providence, R.I. 2007.

Linear stability of homogeneous Ricci solitons, (with Knopf, D. Isenberg, J.). I*nt**. Math. Res. Not. *(2006), Article ID 96253, doi:10.1155/IMRN/2006/96253.

The Fundamental Solution on Manifolds with Time-Dependent Metrics, *Journal of Geometric Analysis*, Vol 12, No. 3, 425-436 (2002).

Stability of the Ricci flow at Ricci-flat metrics, (with D. Knopf, J. Isenberg) *Communications in Analysis and Geometry*, Vol. 10, No. 4, 741-777 (2002).

## Headlines

Dr. Christine Guenther, mathematics professor in the School of Natural Sciences, College of Arts & Sciences, receives prestigious Simons Foundation grant for research collaboration.